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236 ll:i aITEEPA Mep3neK A. r. ra iH. AKaaeMi,rHnr

7) a) Ha rpoMini&y [1; 2] OyHliqin l(n) nprfiMa€ EaiA6inL e ssaqeHHs, nxe aopiB 1, ra HaiiMeEure 3lraqeHlls, nlle aopiBHre ( 1). 6) [-2,5i 1]. Hali6inbure 3Ea.reHss OyHllqii l(') AopilHlo€ 2, a Eai:iMerlxe slra'{el]Hro€

pieeru l:i!{:i:ilii!li{:i

l(r)

AopiBnro€

2, a sanMeHne

ii::liiii:i::.::Ji:i AnTEEPA Mep3ne'( a. f. ra iH. AKaAeMi,{slaf piBeHb ii:l

3Ha-

237

7) = 2; f(1) = 2i f(2,5\ = o,5l 1, roAi^ t = 12; flx) = 2,'to4i x = !1, 3) n(D = t 1; 3l; a) l(r) = 0, nlirro r = 3, r= 1,5,x=1,5,:t=3t 5) l(r) > 0, J{Krr{o r € [ 4; 3),r€ (-1,5;1,5),n€ (3; 4]; l(x) < o, .sr{qo r € (-3; 1,5), J. e (1,5; 3)i

li1:

53. 1)

l,t E; fi

,{) = 0,5;

Oirla cpyg,iqii Ita (42; 0)

6) n(qo r e [ 2;0]ir€ [2;4], 10 rDyHl{IIia flr) 3pocraa. .'IRqo x € [ 4; 2] i x € [0; 2], ro qryriHrri' l(r.) ctraaae; 7) a) [ 3; 2]. HanMeHue 3lraqeFEs (Jyrnrrii l(j') nopirHloe ( 1) Hafi6i"1b e 3EaqFhhr +t Hs /(ir) nop:8hrc. 0. '11

::r

:i .]

11. HanMelrtlle 3HaqeHHn dryHFrrii l(x) aopinHloe ( 1), a Eai:i6irbrre 3Ea-- qncno 2. 3; 1]. HariMeHDe 3tsa\elrH.s dyEIiIIii l(ir) aopiBErc€ ( 1), a Han6inlue SraqeH

6) t-3; .reHH'r

s) [

:.:

qricro

.!i:.:.:L 54. 1) O6,racrlo Btr3Ea'ierllls

2t ftxt

= : .

$yHftIili ili

rilicHi 3HaqeEss

e Bci

J., RpiM .x

Dtf\=17:+-)t

61 /tir) = --1.

lr.

..1.....-

SHa.reliHt OvERiIii l(r.) icHy€, nlrll{o

r.+0a6or+5.ToMyr(r=( *;

5it I 0;-ar.(r. 5) + o; x a.0.

J'-

sHaqeHss OyHKIrii l(Jr) icnye, srrtrro

ro6ro 0 < a < 1. ToMy

r{l) = [0; 1]. . 3 "'FHIs +]hKuii /r"r rrHv.. qKuo 12 4r x'

1 r>0;

[:r <

Jl2 4x x 4x-12<O; 2<r < 6. ToMyD(/)=( 2;6)

t; Oi

Jr-t>0, ,) l(') = *+ sEa.ienH'I oyHnrrii /(r) icsy€, 'iHqo LJ. 1+ 0. To6ro r - 1 > 0, r:' 1. ToMy r(l) = (1i +*). r>0, ro) l(:r) = \G J r. sHa.{eErrs Ov"xqii f(,) icllye, rl{rlo To6ro r = 0. Touv ,(l = {0}. 55.r,/(r) '1.otn ' t+2 2t ltxt

, "6.Dtlt

(-:2) R.6o-t rI

t2i -)6('x,2. 0norr

R-

3j 2 . g.ro r 5r 4 , 0, ro rlaqpHHt /(r., j.q).. 5r+4 5, +4=0). 'roMv ,(f) = (-*; 1) u (4; +-) (6onpr.r= 1i:,.=4srpasr: 3)' /rir) r'

qrfrr, u6rz \r 5.D,/) ts,r-r.oo ]i 238

r::::i

roqna neperrsy rpaoi(a OyHrirrii f(r.) tu Bicclo Or.

T ".*" x

0. ro

iro,

12+3r - =O- 1r=-4. Orxe, L2.r-5*0: Lr=2.5.

roqI{u

2.4. nr(uo

(0t

irrr " o. . lf- 3j

2,1) i (-1i

roqr{u reperlrliv

rioopaiEar.

o(.r)=rE 2. flfiqo

jr = 0, ro (p(0)

-2) i (4; 0)

.r = 4. Orr"e, roqKr (0; MrI Koopartsar,

2. fll{tqo 9(,.) = 0,

,o Ji

z=o: G =2, I (.r) 3 ocfl-

roqftr neperrny .paotua Oyxl{llii

5f + x - 4. gnqoJ. = 0, ro l(0) = -4. flliqo l(.jr) = 0, ro 5r.r + r - 4 = 0i ''0,8; , I OrxP. roqHr(0: l). D I 4 5 l-41 8l:.. r0 lo ( 3 ocsMl't (ooparHar' i 1; 0) ro.rKr repeusy 0) l(r) ryaoi(a oyHllqii t0,8; .r" ly 3r 0, '": '"-. fl*uro )- = 0. n /(0) 0. flKUro /r.rr 0. o 1'' 2) --" r a l' 8,0: ^rt lrrx 3t o, lx 0, (0:0) i( 3i 0) roqKv n"oel ,H\ rpa0"{a tlryHKqri l(r,

I l'=

Lx-8i

roq*"

3 ocrMrr rioopArHar.

(0i 5) u (5i +-).

7) /(x) = \,6 + .f1 ;.

8r /ri)

flxrqo x = 0, ro l(0)

3 ocsMr' RoopaxHar. rpaoi(a dryHlluii '(J.) 3) s(,r) - 5 - r'..ERlro x = 0, ro s(0) = 5. flI{qo s(r) = 0, ro 5 - I,= 0; :r=tJs. orxe, roqru (0; 5), (-./6; 0) i ("6; o) roql(I{ nepernFy rpaoim rDyllrtqii s(r)

57. 1)

60x 7>0, rliqo:,.>

\-j'-i: lo 4r /tr.r= ' ; Dl,t) { -i .1,;{ r I 0,J J-x 1 5) /(:r) = Jr' + 6:lr - ?; ,(D = ( -; 7l'Jl:rt+*), 60 jr'+ 6jr ? > 0, sftrqo n € ( -; zl, iir r-r.

ht.r=1?*

robro

:r-6' . D(f)=R.

s) /(r)=

3 oc.aMn

'i.:{a:'

= 6.Toqna(0; 6) - roqlta repeausy rpa = 0, l(r.) s Biccb oy..tlntqo l(r.)'77 ]-r = s; r = +2. To'r' "o lr-o=0, 6.

56.1, l(.r)=lr

l, l i," t

AnfEEPA Mep3nqK A. f, ra iH. AKaAeMiqHnf pieers j:l:;:i:;:;:i:;:;i:il:ii

58. 1) l(r) = o,ai' 8;

0,4.r 8 = 0; o,4r = 8: x = 2O; 2)s(xr=2a+3:. ," -r2 +3x+ 28=0; rr 3r-28=0;

3 ll D s 4 t r.28r 121: r. 3-I1=7. 22 "" 3),r(r)=v[+4; .it+a=0r r+4=0; r= 4; 4) $lr) =

r'z+r

---;

5) flr.) = r.3 9r; ;rr 9.r = 0; n(irr 9) = 0; r = 0; 6\ eQ) = a' + 4; tc') + 4 = 0, r e Q.

r. = 13i

l) '33 /(/) rr 1.r; rs-1"=0, ' 4;. o.xe. /(xr=u. nx.uo t 2, flr\ = 5r' + 4x 1;sx'z+ 4.r - 1=0j 2*3 l, D-2 i., rr-4.5-9: I. '. 4555 ".'3-l

59.

O,Hp.

flKULo

0.2 i x

uft=o; 4\f(r)= 4trea. a)

^jr) l(r)=rf,'-s;

r'z e=0; .r = 13. or'Ite,

! -0.?{ = or 5 frrr=5-02'r a-2 x 2 x

Orri{e.

flr) -

:;:i:::i:::::::!::::::i:

0, sKrro

45.

0,2J. = 0,

x=25,

= 0,

sxqo

^')

i3.

2+Oi

= 25.

AITEEPA Mep3reK A. r. ra iH. AKaAeMiqH{r piBeHb

:iii:

239

l(:)

=.r'?

r=0,r=-1.

ti t2 + r

= O;

r(r + 1) = 0; r

60.l) g = 7t 3. npoMixHr.r rHakocra-flocri: y > 0, snDro -7t + S>O; 7x> -S; x<!; 7

= 0 a6o

, . (--'

-1. Orxte, i(t)

= 0,

rlcqo

y, y,=-3r,+7 +3\ ', 7= 3(J', a,)<0 @vHriqia v(t) e cna'qnolo. 2'; a@) = 9 - 2t,, SEanaeMo 3) Hexan jr, > r,, ro,qi y(t,) = I x") < 0. ovnxqis v = I - 2jr € craAlrorc. v, h=9 2a,-9+2\=2(t' 4) v = t, Hex ft x,> \ roaj. vk,, = r,t V@) = xr 1\ -.t, < 0. oyEftIlis y(t)€ craAHolo. SHaiAeMo: y, yt= t,-(-rt)= ttll 5r y ;x. Hexan.r, r- rori !(x,\ uG.\ -r.- .r, =;{t, .Y,)>u.

?-)'

y<0,filtnto ?x+3<0; 7x< A; x>?; 2) V - x' at + 16. flpoMbtrrrlr 3EaKocranocri: A>0,f 8r+16>0',(x 4\'>O,t+4:xe ( -;4) u

"(?'.-)

y<O,tea. 6 floori**" 3l ', 4-a

(4; +-);

y > 0, sroqo r. € (-1; 1); y < 0, nKqo t € ( -; -1) u (1; +-). 5) u = Zx'z 7x - 4. IlpomrNnr 3Hakocra,locri: y > O;3t2 7t+4>Oi3x'-7x+4=O,D=7''4

7+1 4 r.=-=-=I '633'6

7-l 1: r^=-=l:

u<0.Uc2-7r+4<O; y > o,.nxrqo r e t -, tr

oyHRuie y(.r) c apocraloqoo. 6) V 2 0.6x. Hexaii x? .r,. roAi vk) - s(r..) = (2 - o,6x") - (2 - 0,6rf) = 0,6is1 0,6', = 0,6(x, (DyHKqii y(r) e ctra,qHoro.

rgarrocranorri:

x 0:x 4itc \@i4)i v 0; =Lr0;4 "4t 0i 4 r 0;x 4; x-(4t -). u.0; " 4t ! x' L npoMiAkl.r 3Haxocranocrj: A>O| *+ 1> 0; (1 ,X1 +t)>0;

63.

< 0.

1)y= 2r+5

11,

3 4=49-4a=Ii

---+-\---

**), " (t|,

-3n1 = 1=e.s. = " =-91= r.,^'-42

-\],',r

+ 3x + 1 = O,

,(t)

= 0,

sriqo -2r +

61. 1) y = 0,6t + 12. IlpoMiri(u sHarcocranocril 0,6x + 12 > 0; O,6x> -12i r > 20. Orxe, y > 0,6Rtqo 0,6r+12 <Ot0,6r < -12i I < 20. Orr{ie, y < 0, s&qo h U =,18 ' 3, tlpoMinxu rflakocra-ro.ri:

5>0,)c<2,5, ro6ror€(-;2,5); A < O, t> 2,5, ro6ro Jl: e (2,5; +-)i 6) y > 0, "sRrro -2x + B) OyHI(qis y(t)

€ cra,qHolo.

3) g=2

a) 6)

l]>0,re (-*;0);y<0,t€

OyEriqi.r

y(r)

(0;

+-);

€ cnaAEoro.

t € (-20; +-); jl: € (--; -20).

y>0; G+3>0; r20. Ornie, y>0, sRqox€ [0; +-); g<OtreA. 3t g = 9x - x'. flpoMi)rrKr 3Hel{ocra-'Iocri: _/-T=\,.------1,-y > Oi 9t - t2 > O; r(9 -.r) > 0. Or!(e., > 0. i----(9i *i ---\ +-l ( or J (0: 0. txqo r.. r c 9) i3, tl(qo 4l g 4x' 3x - 1. flpoMiJ{rHx 3saKocra"loc'i: u > O, axnto 4x'- 3x - 1> 0; D=3'- 4 4 ( 1)-25i

a)y(a)=O,reO; 6)u=2>O,xeR rpoMir{RiB B) y(r) - crara OyHrcqis, 3pocralll{fi i clla,qaEHs EeMa€. a\g(x)=O,xeA' 6)y>0,a1cflrot€(-;0); y < 0, nREIo t € (0; +-);

-->j--_}4

_3-r ._ 3-5=r,, ^' s -' i' s _o.zl.

B) dysK4ra

-o,25

iH.

AKaseMi,{srai piBet"

{i;::li$tilrli

v(t) spocrae,

sllqote ( €; 0)ixe (0;+-).

r € (-*; 0,25)u(1; +*),rog> 0..Exqor€ ( 0,25;1), roy<0.

fli: AITEEPA Mep3rrKA. r. ra

5 = 0;

= 2,5i

----\,.'-i-\/----i-.j -----;

Orxie, y > 0, s&qo jr € (0,5; 1)iy < 0, €lcrro r € (-*; 0,5) u (1; +-).

24o

- r,)

.+-

y<0,'xrqo ".{.'''*J. 6) V = Zr" + 8Jc - 1. IlpoMi*{rin at u*o".-o"ti, a>U 2f+ 3t- 1>0iy<0; -2x'z + 3t + 1 < O: -zx'z D=s-4 (-2\.( 1)=9-8=1;

grinro

62. 1) Hexan t, > t| Ma€Mo 10t, 3 10t1 + 3 = 10(t, - ,r) > 0 roAi 10r, 3 > 10t1 3, ro6ro OyHRqis y = lot - 3 e 3pocralo.{orc. 2)g= 3r+ 7. Hexaii > ,t, roai g(',)= 3',+ 7iy(r',)=-8tt+T SEaiaeMo:

;:iiiiiiil:iillii uresPA

Mep3nrK A. r. ra iH. A(aaeMi.rHran piBeHb

ii:::

241

t"i fti

5\s=x'+2,

a=2r

65.'t) s = l(x)

/(r)=0,flnrqof= 3i,.=4;

!=e(J)

e(:r) = 0, anrqo :t

= 2, x = 0, :. = 3.

Et! El:

,ji

a) y(r)=0;

i:l

r=1;

r.i+2.' 3=0i.r=

3a6o

r.(2

"r' 21 3 > 0, s(rqo r - ( -r 3) (l: --r: ir' 2.ir 3 srtrqore ( 3;1);

6) .r'

t.:.:.!!ii!l I.r:.ii!:.i:.:

ti!l!!!i!i

OyHXITiE

y(r)

l) q=3

I 4

2r r'=

rl:)

r € (0; 2)i

66.y=l(rc),x€[-6;5].

, e (--i

0) !, (2i +-); B) OyH:iqi' ,(J.) 3pocrae, nxrqo

r € ( €; 11, OyIIIlqifl r(r) sklroxe [1;+-)

3Poc.a..

= 0, ro6ro r = 0 a6o r = 2; > 0, s.asto 2x - x'z> 0; .ir(2 t)>0;

y < 0, nlirqo

cnaAae, slcqo

rq /,1x) r ( -: Il. 'trvHK E(iqot€ [ l;+-).

64.

a) y(,.) = 0, sErqo

l(:,.) = 0, slinlo r. = --6,

cna,qae,

67.y=f(r),ae | 5; al. 1).trl{qox€[5;1], dlyExrrifl l(x) 3pocrae; sRrlojr e [1; 41, drylrl{qis

: !x=o: r=12:

a) y=o,snrro

6) r> 0, flrirro xe ('*1 12\; a < slrqo , e (12; +-); B) cpyEl{qiJ{ cEaaa€, sllnlo r. E

3\v= a"+ 4x

B) rDyHnqis cnaaae, .snqo

i.T€(0;+-).

-q.

6a.-r=/(r),re

al U=o, xe ai 6) y> 0, jr€ (0; +-); y<0, ir€ ( -i

s=9

t €(

0); -; 0)

e [-5; -1] i [2; 41, Oyrr( qis'Iriqo., cnaAa€. OyHriqis 3pocrae, n{rqo x e I t;21. 2)

-R.

(DynRqis 3pocrae,

sl{uro ir €

( -; 2l i [0; 3].

(DyHkrrir craAae,

Eri!{or€ [ 2;0]i[3j +*).

r'z

r l" tro. lt,t. (l; -); l) /(r, r I J,; IL.r-U: 1'-U: Dllt l0; lJ 11 2) flx)=-+-i x'! 1 + O, x + :tl; r' + 3x + 2 + 0i x + li:t+ a' I a'+3r+Z

69.

,(/)=( -; 2)L.J( 2; 1)U( a)

r=0,sl{qor=1ix=3; 6)y>o,ir€(1;3); a <0,x. ( -i 1)u(3; +-);

a) 9=0, r=13; 6) y>0,'nnloJ'E

B) dlyHr.iqin y(jr) spocrae, sriu.ro i.

snqo

€

( -;

21,

Oylrnqir y(.') cra{a€,

r € [2; +-).

242 ,;t* A'.IEEPA Mep3neKA,

1)L,(1;+-);

3) ft"t= t '!:' 2.1 -r-2

( 3;3)iy<o,sHqo

jr € (-*; 3) u (3; +-); B) OvE(qifl 3pocrae, .sl(qo ,. E ( -; 01, OyHriqiE cflaAae, ERllo jr € [0; +-)

ra iH' AKaIleMl9H14t'l plBeHb,ii!i:.ii:.iiii:

;

4t ' It4 2"*1=\15-7r2x l-3=o' r-3 lttttx zt

2a'1 7x-15<o:

::iai;:::!iii;!lii: AIrEEPA Mep3nck A. r. ra iH. AKaAeMi.rHht piBeHh

i:i::: 243

lili

- o,tre.r. - I1.5:3r

l(,)

t(,) = {

4) i(jr) =

6}.

J13:51.

OysRqiI

l'l

t(jr)

3. o6,racrE 3Fa.reHb = I 3; +*).

2x' 7x 15=O; D= 49 + l2O=169i 7-15 3 -1+lA .rr=-=5:

st ft'l=uE,4

*,1;

s,.

* 7:

xz4. llx<1.

l2r 8>0. I 8r+720: lr' l-_, tL^ _

1--a

i:ri:.i!i!!:

r' 8x+7=0:1" " i,=1.

-1

Ofliie,r€ [7i +-).

. o, ["<o

fr>0. J,-0, a6o Ix.o. 6) /rr) Jl,r -ir; lrl - r '0: I lx .r " u^ [.r x>0: lo r>o Orn|e,r€ ( -; o)Uf0i+-)=( -; +-)=R.

70.rr 2t

l.r

l(,) - !t-1 +!5-;

f(r) = x, + 4x + 8t f(r') = (r + 2t, + 4.

t(i.]) = {o}.

KoopArEarr BepurEq t"

E(a) = l4t +*\. 8) /(t) = -r': -

o.*., !' I ti4) )t4: +-) /rrr J*-r. 3a 1r'l'0 1' Lr 4,0: l.rFa.''

J-x : Etr)= \oj.

2.1

nBir(sr

-2, g. = 4, iBirrcr' rapa6orr

2r + 5. ItoopArEarx

Beprxtrnu napa6onqi

l a= (-1)'-2 r'l).5

napa6ons cnp.nMoBaEi

72. 7) f(x) = 4 Jrc;

t(') = (--;

BHr.r3,

al.

[tr\ x'-5x-4 '- '-, 1' ' ",A' ., {f ,]; lx +5x

cnpsMoDaHi Bropy, roMy

roMy

lr2 5 6. = t -; 6l2) f(t) = t, - 6r; fG.) = A:t 6). ,"= 9=s,v.=-g,r(t=t s; +*).

t(jr)

..x, tt trt3 -,, -ot. lr, 5.x 4=oiD. 25 16 .9: r.. ';t ". O\xe, D(f) - I-2: -1)u( 1; +-). ir<0, 3r [-x : 0' l'< o' 3) f{jr) =./_-t ffi, ]+ ,,,0; (2 r)(2 + r) > 0; ) z.'.2; rc

(

01.

d) /r.r, = r.

€

71.1)

{ -i

orxie, ,(D =

01.

t/6'

16 x-o' \6 , , ,.'2u-, l:"]r;";., ;,;1.,- r, :l; ]l; 0)

u (0i 6). or}I€,

f(i=G+2.

Oyr.Errii

(

I](,)

D(D =

( *;

O6nac1.L snaqeIIb

!r (0; 6).

2) flx) =

73. U DrlJ=R, Hpivr.=-2,

x'|;

E(r, = (

71.

= [2;

D(fl = ( q

/t*t

,--..l--. (,r + z)(,r 3)

Hanprliraa: l@) = Js - x.

3t ::i:::i::::::::i:::i::::j

t5:

D(f) ( *: IJ J (

4 D(n

tii:: AJIIEEPA Mep3nrK A. f. ra iH. AKaaeMi.rHlan piBeHb

HanprrKna,a:

J'*.4 --1. Hanp KnBn: Ittl " 4) DO = I ll.Harpunnaa: n, = V' -, - r. "-j-, 3t DUt=l-4:5r

74. t)

244

31.

r=3.

( -;7).

0) (0;

HaEprnnaa:

1,. Hanpr.aKna,q: /(x,

(x + 1Xx 1)r

ftrt = -!. J-,.?

DUt=l2i5r J (5: tjr L {tjr '-).

Hanpnx,ran:

/(.y)

l: -. {x c)tx' b)

:iilil::ti;i::.:i::J A'TEEPA Mep3fle( A. r. ra irl. AKaAeMi,{Hnn piaenr

lilj

245

75. 1) Hi.

3) raR.

2) TaK.

(Birllnr

crpEMoBaHi eropy, 60 d = 1, 1 > 0, rpaoiIi repernHa€ Bicb Or y ro.tEax y (0; -2). 1; 0) i (2; 0), a Bic! Oy - ro.rqi fpaoixoM Oy:rRrlii y3 = 2 r e npsLtd. l(r.) = 0, sltqo r = -6, t = -1, x = 2; /(r)>0,.sRrrrore ( 6; 1); flr) < 0, anrqo r' € ( -; 6)u( 1;2)u(2; +-).

(

iDyHxuir

r--: -2r i (l:

rpo.lac

2|.

I 2: ;li (2t *).

,Dyr.{uir coarac Ha ,povi1lr"ax

[r:+2r.gxruo:<0.

roai a,'ls 6yar,-sno.o sHaqeHEs , icHy€ ABa pisssx sriaqel]Hs y, lro He BiArroBiAa€ BnsFaqeHslo oyEnqii. 5)

4) Tan. n.

Hi,

;:,iil:.i:.:.:{

lr:.!alt:.1.1n 1.:-':.i!]1i:.:{

l'ilt i.!i:.i-i:. ti:ii-l:.i!-ai:.:

2') IGJ = I lr.' -

2r.. eKuro r. > 0.

)c2 2t e napa6onn, (Birllr' nxrx crpsMosaHi Bropy, 60 a > 0, a nepfinrnaua e iovxr (-1; -1) i (1; -1) siaroBiaEo. l{r) = 0, sKu{o r = -2, r = o, z = 2. l(;r) > 0, suro .r e (-*; -2) u (2; +-). l(r) < 0, flflrqo r € (-2; 0) u (0; 2). oyn(qis craaa€ l]a npoMirn(ax ( 11, (0; 11. fpaon{oM OyH}iqiii y, = t2 + 2rc i g2 =

.Dysl(qis opocrae H npoMix$ax

lt*:.i:llll

l8 .rnax< I 78. ftxt

[

1; 0], 11; +-).

l2x' - a- qKlo- 2 s x = 2. ^ I .sr{4n>z.

RR u, --tx i !r, - .rilpp 6oJrrr, a rpAOi{oM OyH:1'\i\ y,= 2tr 4 e napa6ona s BepIIIrHoro ! ro.rqi (0i -4). f

lx+I.ekuox< 1. lr' l. sxuro .r : 1. l) f( 2\= 2+1=-1,60( 2) sa,qoBonbsse vMoBv ir < 1; l( 1)=( 1F-1=1 1=o,60( 1) ra.qoBonbEs€ yMo 3yn> 1; /(0) = 0e 1= 1, 60 0 3aaoBonbnse yMoBy r > -1; f(2t = 2' 1=a 1 = 3, 6o 2 :a,qopoasn.a€ yMoBy x > -1. 2) f(x\ = o, .a(qo = 1; l(r) > 0, nKu{o, €' (1; +*); l(r) < 0, sKqote( *; 1)L.,( 1;1). OvExrris i(jr) spocrae lra npoMirriKax ( *; 1), [0; +-). oylrr{qis l(r) cra,qa€ Ha npoMixrxy [-1; 0].

76. ftx) ', ^

[r+6.rnuor<

ltx\ = 1r r x. sxuro - 2 1 "r < 2. [2 -.r. FKU{o .{ > 2. IpaoixoM OyEllqii Yr =, + 6 e rpsMa. IpaoirioM OyHKtIii U,= t" t - 2 € tapa5ona,

77.

11 24) r\ (t" A\rt /tl'z t 1= 1 I 1 -l 2 ", = \21 4 - 2 -2=-2-\-4

r sepuuHoo B'ro.,u.i

246 lii: AIrESPA.Mep3ncK

-r

2=1.

A. r. ra iH. AkaaeMi,{Hrfi piEeHb ,iii:':,i;i:iitlil!

pdoirov OyHRrrifi

f(x) = o.,tr"DJo' = -2, k = 2. i(r) > 0, n}lqo r € (-*; -2) u (2i +-). l(r) < 0, sllqo r e (-2i 2)...

OyIIKrris l(r) spocrae Ha rpoMidiEax (--i -2) i [0: 2]. OyHXuin /(i.) .naqac Ha npoMi]{Kax [ 2; o] i (2; +-).

79,

l) u=-:-:-,.r L [2:5|. O)HKuifl :t'

Bosa 3pocrae, roMy Ean6irbnre qe y(2) = 5.

2) a =

to )c e ol. oyurqra g I10 = -,x.x lz;qe

aoMv sQ)

=.5

AO-g= t'+61

FenepepBEa, Ea rpoMfun&y

aG\ =

[2; 5]

-2, a HafiMel xe 3HaqeII-

lrenepepBlra, Ha npoMilR&y [2; 5] craaae,

Ean6irbrre BI{aqeIrHs, a y(5) =

qe IIaiMeIIllIe 3Ea.renHs.

E [1; 2]. (DyHI(qis ! = r'+ 61 7 - EerepepBEa, Ha trpoMiri{fty [1; 2] spocra€, rpaoiKoM e rapa6ona B BepmrEoro B ro.rqi (3; 2), iBirnrr cnpsMoBaEi Bslrs, 60 a=-1,-1 < 0. ToMy Hafi6inr,ure BEaqeHHn \e v(2\= 4+12 7=1,asafiuesme qe y(1) = -1 + 6- 7 = -2,6(r.' = 3 He Hane,'irrb rpoMi,riEy [1;2]. 2), € t1; 41. IIboMy rpoMix{(y Eane}I{'arb il: = 3, roMy y(3) = 2 € Ilaii6inblnuM 3Ha.{eEHnM OyHxrrii. IopiBHneMo 3HaqeHHn aG) = -2 i a@\ = 1. HanMeEtlle 3rra.reHHs 1)

v\t)

:::::il:iiltti::lt: A'TEEPA Mep3nsK A. f. ra

iH.

aKaaeMi,{Hnr piE,eF.b iitlti:. 247

3) n e [4; 5]. Ha qboruy npoMiJ(I(y senep€pBEa Oyrliqis cra.qa€, roMy y(4) = I 6inr,mrM 3IIaceHHsM, a y(5) npoMi'{llly [1; 4].

€ Han60 x = 3 He EanealrrrL

safiMeslllr

81-y=)t'+2, 8 1) , € [ 5; 2]. Ha rrBoMy rpoMixrRy oyrHrris EenepepBrra i cna.qae, a6cq{ca B€pIIIuIrH Mpa6orq x, He Hajexnrb raHoMy npoMrlr{K). rov} Ul s, 25 l0 8=-7 ; -l e Ean6inbme 3HaqeEHn, avC2\= 4- 4 8= 8 e llanMeEnle sEa.reHlrs. 2, xe [-5i 1]. A6cqrca Bepr x r napa6oJrlI n = 1llane]iillrb qr,oMy rpoMinc&y, {sirKu, trapa6onn crpsMoBaHi Bropy, loMy y( 1)= 1 2 - 8 = -g e HaiiMeHrie snaqeElrs OyErsrris. flopiB$seMo 3Ee.reHHs v( 5\ = 7 i y( 2) = 8. Han6inb e 3HaqelrHs = 7. - 4e31.y(-5) 3) r. 6 Ha qboMy rpoMir{rcy HenepepBEa ibyHnrriF spocrae, rs = 1 He Hane[0;

rnr{rL rrEoMy rpoMi:riliy, roMy y(0) =

-8

e HaftMeErrnM sHaqesEsM, a y(3) = 7 € Han-

Oi 21, + 25if t to 28t2b D - la - 2\' - 4 . 1 ..25 = a' - 4a + 4 - IOO = a.'z 4a 96. Ans roro, rqo6 Aaxa Orflrlliis Mana ABa Eyni, rpe6a, qo6 o? 40 96 > 0. Po3B'g}I{eMo qro EepiBnicr!: a' 4a 96 = 0:

g = x,

D=4-96=roo: o.=2--i!=n o^ 2 to 8. 4'1 1 Or}r{e,.El{rqo a < -8 a6oa > 12, aalla ibynxqis y = t'+ (a 2'), + 25 Mae A3a Eyni.

fllrqo:> ABa

Eyri.

piBHrEHr (1)

oo 9, o, 7-3 9-qs 4'1

tlpr o € ( -; A3. 1, a =

u (10; +-)

zt'z 2(a 6\r+a 2-

Ma€ ABa Kop€Ei, a Cryrfl{qis y =

Po3B'ndieMo HepiBHic?b

o? l4a + 40 > O) a'

tot a, 7-? -4. '

AaEa Oynnqiot

r' + (a - 1rr. + 1 - a 1)r+1-a-a'=O

a'!

ru"

auu

14a + 40 =

(*li

(1). ''z+(a IIe piBssnHr Mae ne 6inblne oAIIoro llopeEfl, nKqo, < 0, a AaHe piBffrflra (*) Ma€ He 6in6tne oAnoro Hy,rs. D=(a t\' 4.1.(1 a - a'\ = a' - 2a + 1 - 4 + 4a + 4a'z = 6az + 2a 3. PocB'&rceMo rlepiBtricr:. \at + 2a 3 < 0.

50 | 2a 3 0; -4

l-5 (-3J=l-15=16;

=-]4=!=o.s. " =-l:!=

flpr

2) '4 u -1 x" -sax -9a -8a 1

- 4 x'

+ sax

- 9a' - 8a = 0

-1

6irL

e oaHoro

0,6

Hynr.

>0.60k

6inbl]re

y,l,oBtt (2) a"

> r",

^rt

r",

un"

-3----;:------; (lr,l < :c1), roai:

rt-x2

tr.a

xr2 o

{lr.

Heiaii jrt € (0; +€) i r, € (0i +-), ,, > r| roAi: h \)>o,6('h>0,)r2 x2>oixf2>o -t =h(t" xtt"

(2).

L, L. rt

L ,L

orrrre, Ans t, > ,r MaeMo V, < y1, ro6ro (,-; 0) i (o; +-).

L op, * > 0 cnsqa€

Ha npoMix{Kax

,=!. u. o.r.c r-@:o)u{o:-a) 60k<O,x, ,r>Oir1r,>0. Bpocra€ lra rpoMi'Iiriy ( -; 0).

az rt>

€ (0; +-) i O

i rJ,>

Ha rpoMinRy (0;

MaeMo:

e (0; +-), x, >

O. Ma€Mo:

x, <

,"""^,

'')<O,

-k =k("

i r(r,) < y{x,). ro6ro ,=L,

+-+=u':,;''th

< r.? i 9(.tr) < y(x,), ro6ro y

U.O

<0,60*<0,

=:, k.0

spocra€

+-).

85. y = i(r) - ctra,qEa Oylrxqis. 1) a = sflr). IJexan \i x2ha.re:!l,aat D(g) i x2> tr ron\1f(r,) - gf(t)= 8(flt,)<o, 60 f(12) < f(t), ockuttLn f(t) cnaAsa abyEnqis. Or*e, y = 8l(x) cransa OyEx^x,D qi.n

(3/(r,) < }f(x) 1

2t y=;ftrl.

'rp*r

x,> xr x,e D(vli.\e

D(a)r.

AEanori.{Ei Mipr{yBaIIH.n ao3Bonsrorb 3po6rrrr BucI{oBoI{, rqo .Eansa OyHqqin, ocki,rERr ra yMoBoo

n"r)

- cnaaHa OyHKqifl.

3) y = -l(jr). Hexert tr i ,, HaneBarb D(A) i t,> xr rIopiBHs€Mo y(1,) i y(r,\t a@ ) - ek ) = - f(r,\ - (- f@ )) = - flr,) + f(r ) =, ) flr,) > o. Eo y = l(r) cnaAHa, An" tr< tc2, f@,')> f@"'), s(n\o \e D(A), r,e D(y)r, orrKe, y(x,) -> y(x,) rp h> xr'roMy u=-f(r) spocralo.ra Oyl{Itlri.r. da. y =

(1).

til: AIrEEPA Mep3rqKA. r. ra

-8a =16a'1-8a;

(*J:

6irbure oruol.o Ryna.

248

!. !.

o'*.:...^'

u .tt(n

Ue piBEssEs Ma€ ne 6irErre oalroro ftopeHs,.aftrqo, s 0, a aaHe piBEsHEs (*) Mae HF

(--; o) u (o; +-). Hexafi r, € (--; 0) i r, E (-*; 0), x, > r,

a € [-1; 0,6] aalle &ys&qis (*) Ma€ se

-ga

a4. a = L, h> o, x €

Hexan

=\-,--:>6-'

rrv,"i.

go' -aa)=25a

HexaEt,€ ( 6; 0)it,€(-;0),r,,r,(t,<n,),roAi

2, a = 2x' + 2(a - 6)x + a - 2i %c' 2(a 6\!+ a 2=o; (1) 2=g-Ay 2@ 2).o, tza t 36 2at4 ar t4aa 40. D

D < 0; L6a'z - ia < O;84(2o - 1) < 0i nDn a € [0; 0,5] naHa Oyll&qi.s (*) Ma€ He

3 yMoBr (1)

6inErrr.rM sIta.reIIEsM.

A2.l)

D 25a' 4 l\ +l 4' I

iH.

AKaaeMiqHrf piaenr i;ii:liiii:i:ilijl:l

l) y

11/1

3pocraroqa OyIIKqis.

,ftrr. Hexaiir.. D\gl.x,- DIUILx,.xr 3a yMoBoro y = i(r) Bpocraroira ibyEnqin, ro6ro /(r,) > l(r,). :i{::!i:a.:1i::.iti{a

(1)

AITEEPA Mep3reK A. r. ra iH. AKaAeMiqHrat piBeHb

l:;..i 249

lll el'3iilrn ;ltxtt - rlt r,t ztftxtt-ltx rr' 0,603yMoBu fl',) > fG).IIe ossa.ra€, qo y(',) < y(',\ lplj r, < t, g t_ rpo.rarcqa

(1)

Po3r,rsHeMo

se"

r; n';1={:35=o D(f) =

lotrfo

Qytlr(urs. 2llrt 2ty zltxt.Hpxanrt- DtAt, x2c DIC)r r. x. 3a yMoBoro, = l(') - 3pocraroqa (DyEEqi.', ro6ro fl',) > f(Jrr) (1). Ilopiesr€Mo ptusxqrc aQ.,, ve) s EyneM nns OyElclrii y = -21(t). ( 2f(,,tt = 2^!j) + zflx,\ = 2(f(':,) MaeMo: e(',) a@,\ = 2f(r) or,fte, y(,,) > aG) i xt < x,,'t e D(!), n' € D(y)' m6ro v = -21(')

j[l*rt=

. 12x + 48 12tx + 4\ 2) Ilx)=-=-=-, .ir' + 4.x jr(r + 4) .f,ltrqo

( *;

D('

u (5; +*).

r r 4i.r.*0; ( -; 4) \.r ( 4; o) u

f(x1)) > o. e ctraaEoro

x(zm 20) + 6 (*). (') 6yna spocraloqon, noBIrHIra BtKoEyBarlrcn BIrMora ,4n.a HaiiMesne qine 3lia'reslt.': n'3. IIpan=3 7n 20>O.tn>zO: n>29. 7 + Imt 6 20, € spocraloqorc' = OyHllqi.n, roro, qo6

dpyHnqi.a

(*). 2k + 3 + 6') A = x(h + 6, - 2k + 3 Ann roro, qo6 {byHriai! (*) 6yna cna{Horo, roBuEHa Birl{oHyBar'ics BlrMora k + 6 < 0; * < 6. Or;ne, npl':&€ (--; 6)OylrKqifly=kt 2&+ 3 +6recnaaHolo

88.!=h'

89.V=3x' bt+t,x e [3; +*). SHanAeMo t. 3pocrae ra rpoMiniliy [t"; +-), 60 (BirKn ro*u'6 4<a. asra. Or]{(e, rpr D e ( -; 181OynKIIis y = 3ir'

= *= Z

oy',.qin

3,'z b'

trapa6o.Ilr EarpnMneEi Bropy.

bb 90.a=tu-4x', a€[ 1; +-). SEaiAeMo ' 2 (-4\ 8 (DyExrris y = b]. 4x'zctra,qa€ Ea rpoMit*ry [t"; +-), 60 lBirr$rr napa6onE sarp.sMg. neHi uEE3. ToMv l. -r. a "8 = Or*{p, trpr b € (-*; 8l OyHRqin y = rir 4jr'?cna,qae Ha npoMi}Itftv [-1; +*). lSir c

91.y=-0.6r

Brxoaqqr s roro, rqo a

92.s=2r'

Hxuin r+) aocrrd. npu

i Hai,r.

.r.

iBirnl{' sKoi EatrpsMnelri -12

3a yMoBoro EanMernne sEaqeEEn OyElrqil (*) aopiBEroe

(

roMy-3=2.9

25o l*

O) HHujfl

np{iva. B ro,rui ,"

Bropv, roMv EaiiMeH-

22 " 3),

12 3+c;c= 3 18+36=15.

ATTEEPA

iln:::::.fl|

3) l(x) = ::-

l:::::::].:ft|

4l llrl=

3t-+ r+1

(.{+1Xx-4)

fpaoilioM dpysnqil € npsMa, nlia napanenbHa oci Or i He Micrr]rb roqoll ( 4; 1) i (4; 1). D(f) = ( -i 4)\r( 4) \r ( 4i 4) u (4t +*).

bl ll.r)

2x'1+5x+2 a'z+4x -_--=-

2(x + 2')(x + O,5l _

x+2

fiErr{or*0,r*

12r'+c(*).

IpaOiRoM Oyn(qii (*) e napa6o,la, nre rHaqe{Ht

:!ii:-:ii$i

r +1

r+ 1.D(f)=( -; 1)\,( 1;+-). rpaoikoM € npsMa y = r. 4, nlta Fe MicrnrE ro.rl(r' ( r; 5).

(*). 0,6 < 0, ro <Birnltt rapa6orlr HarptMneEi Blrus

3 - 2. +( 0,6\ - 0,6 ^'" 2a 3a yMoDoro BHaqeEns OyIIXqii (*) B rrin roqlii AopiBErc€ 2, roMy 2 = 0,6r' + 18ir + c' a6o 2 = -0,6 . 225 + 18 15+c;c= 133. 6in6-e ruaqeHan

.-r'*-r--.111

i:.:':i1:j-{l

IpaoixoM OyHKqii o== e rp.t Ma, sl{a reperr.rEa€ Bicb Or v (-5; 0), a Bicb Oy y ro.rqi (0i 5) npoxon y ro.rqi (5; 10).

flr'nJox+4,r*-4.

D, + 1 rpocrs€ sa npoMitnlly [3; +-).

(0; +*)-

Ipa&iftoM € rinep6ona, (sir&Er srioi 1re Micrfr6 roqiiy ( 4; 3).

OyEliqi€Io.

87.s=Inr+ 6-20rt

MeFTKa.

r. ra iH, AKaaeMi.{H}ri piBeHb Lil;iili:i:;::::i

x(r

+ 4\

2x, + 5x + 2 = Oi D = 25

16 = 9:

,="3-2.,=!a3=6.5, '4',4

*t 2) u ( 2; 0) u (0; +*). fpaoiftoM Aarioi Oystr4ii € ripsMa y = r flria Ee MicrlrrB ro.rok ( 2; 5) i (0; 3).

D(f, = (

::al:i:i:::::{::::* ATTEEPA Mep3rcKA. r. ra iH. AKaaeMi,{Hr4n piBeHb

::::i:

251

'l 6)

l{r)=-

lx 2\r! + 4t ' + 2x.-=r-+zx+4. t-2

i € t-2r +ar. =,;. Hexa; r, i x, Eanexarb rpoMix{fty (-2; +-),,!.. > r.. 4 4 A:L:]-jyL 2t 4t)t 2-x 2tt\x) It,.) .t .2 x..Z |x, . 2\x._2t lxt_2|)r A 4(x. r.t -r', 0 r'' 2 0 r'-2 0' rr, 2rr 2it0 60'r or,lte, l(.rr) > fo) p4 i Hanex(ar! npoMixKy ( 2; --), ro6ro ', I l,*r= ,,, c .rr3nHorc qbvjrKui.'o rra asHoMy npoMi,+(Ky.

95- 1r f(jrr

D(l) = (

-; 2) u (2; +*). IpaoixoM .aaHoi OyExqii e rapa6ona y = .t: + 2r. + :1, sepuuHa snoi 3HaxoAr.rrbcrr B roqqi (-l; 3), a (Bir(r' rranpsM,'reni Bropy. Ilapa6o,la r{e Micrrrrb ro.rlln (2; t2).

8'+ 10, i€ (--; al. Hexan _rr -.r,, h,l , k,i r.,, € (_@; .11 fG)=-r. .r - I 41. Ilxtt fix t. -ni S.r ' t0 - { x- 6,r, tO, --: +.r0+.ri + 8Jr- - ro= .,', /tr,) ,.8r., 'i:xi * e1"" *,y = 1',. -,,1(r, + r, + 8) > 0, rooro ltr,t. Orxe, /(r) = r, - 8r + 10 - craAHa OyH&qir, F&u{o r € (_-; 4). gz. f(x)=G. ,(D = t0; +-)- Hexan xt e Dlf\, r" e DU) i r: , x,, roai tG,) - fl') = .,!\ - !'t < 0. MaeMo /(.r,) < /(r,). 2)

s4-tr,r,r= r +4n+4_I1 != r +2 r-l (' (jr +-2)i 1X' + 1) _ t+2 ir 1 x+2-(x+ 1)=n+2 r. 1=1, D( =( *; 2)u( 2j 1) u

(1; +-).

fpaoixoM aaHoi $yEklrii e npaMa y = 1, gl{a He Micrnr}, ro.rox (-2j 1) i (1; 1).

2r: - rt 2t I(I)=-=

r:tz - rt

r',

=!2-')=2r-

*t 0) v (0; +-). fpaibiEoM aaEoi rDyHXrrii e napa6ona ,ro'rKa V = x2 + he, BeprxuHoro rrcoi e (1; 1), a *airxq" HanptM-,lesi BH 3,60 a = -l < 0. lpaoili se Micrtrr! To.rKr D(n = (

(0;0).

Orxe, l(;r) = yG 98.

r)9=f(r), r€

(3.2\.

.. .*'

5 -(irl

-r' + 4r:

1)(,r': r 5)

= t* 1x*+t, "rr =12+5,r.*-1,x+I.

4'=

\ *: -1) u (-1; l) u (1i +*). fpaoil.oM AaHoi dlyExqii € napa6ona,

D(a) =

B€prxxHoro sKoi € roqKa (0; 5), iBirK," tranpsMneEi Bropy, 60 a = 1 > 0. rpaoiK

lre Micrurb ro'roK

(-1;

(1; 6).

l(r) 3pocrarcqa OyHI{qis, f(r) > O Epu r e re. BBiacv npu ,, > ,, Ma€Mo l(r,) > l{r,), -ae r, € R i .x, € .q. gEanaeMo l,(r,) f(;r") i noptnraevo": uyneM..f{ir,} - llr,) = rfl}tr - ft.xz[tf(rt + fljr")) < 0, roaro f(r,)-< /:(,,), rovy y = f.(!) - 3pocrRe Ha MHolRxHi R. .r c R. OcKirlxx fixl .O. A |txl Jpocrao,ra SyHKuir. lrrr, \o f(x,) > f(r), sxu{o rj € .R, 12e R, ,-2> rct.IIopiBHr€Mo 3 HyneM pi3xHqro: I 1 I\x,)-l\x.) ^ , <u roolo v 1 tr,,t i,,t=-i',tr'. /(t "n*u'HaMHoxHHiR t) s=.rti@, r€ R. ocIltnLRE f(t) > oi s = l(.r) spocraroqa OyHkqin, ao t(:(tl > Ilxtl npn .r, - r| Ae rr e R, r, e R. IlopirnseMo e ry.nelr pta"s,r-, ,,!lr'.r .,ln'"t. o. 1o6.to u - ,,f;Gr .po"'u, Ha MHoxrrHj n. 99. 1) Oclcinllcu V = f(x) Ha MHoxnEi rR € rpocraroqorc ii npr qLoMy /(:r) < 0. ro npr ). r, Lrj € R) flr,l < l(jrr). AaEo rbyHxrrirc, = f(,).-BHaiiAeMo: l'txtt f'lx,J = (fG t\ ftx,l\ftr\t + l(',)) > 0, ro6ro /:(rr) > f(rr,) trpn ,r < ,,. 01)t(e. y = /itrt ue cnalHa OyHnuir. I 2l g = ,r € R. BiAoMo, rqo /rnl < 0, OysRr{ifl V = l(.r) 3pocraloqa {DyHxlD ). qis Ha Mllo,rlulri R, ro6ro anr ,rr € R i jr, > .!, BlrioHy€rLcs piBHicrb /(x,) > l(-r,). llt') 1",' nopiBHrr\o J lrynFM pi.rn"u,o, -r .. I J ,-1 Ir.\ Iktl /{jr,l/tx.r -o-,no,n- ltx.t l\.t,t 1 or*e, anr x. < jr. Ma€rro I r I roMy y=qe

-.*'

100.y = l(r.) + s(:tl, OcRirEKu 3a

252

::::::

AIrEEPA Mep3rsK A. f. ra

iH, AxaAeMi,{Hnn

pigerr

i:i::.:li:$iii:i:i:::i

snuro, € [0; +-).

3a yMo3oro y =

,,-t ,

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Bpocrae,

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r,,

cnaA{a OyuftrriE.

e M.

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AKaAeMieHri piBeHb ::i::t 253

+ (s('r) c(jr:)<0' a(j.,) s(x,) = /(',) r c(r',) flr,j,) - c(j.,) = (flr'') tt('x)) U ovv'l'v 'ui' i v''r i t' x' ,ou,olr,,r ttjr r. or)v".ir " 'rr't , /rr) atr) ,rjo' rr, '' Yro rn tZ II c ttocitt M flKUro t' > i''' ro i" d,vsxqi; /(n) i e(x) 3poc"'nr. F' MHoxnHi ftr ",*.'.'. | > ftx t i El:r^t ' llx.) AoAaloTti ro'rnelrHo ocratrHi tsepiBrrocri' oaepxvcMo e 3pocraloqoto ovrx' i

BnpaBu.qng noBropeHHg

pi3Exqlo:

ii':i r J,'1, ii',r rt' , ui, ro rra

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107. 21

d'jvHkuii i r., e NI, x,> x\, roai l{r') -: l(jr,)' c('') < s(:'r)'<5() ciaa}Ii na;Ilo,1!trrli 'vr' ea vMoaoio 1ir; -' o' eG) 0 no8eac i y = ct,l pr3E' ,f,u""uj" y = /(') s(') e spocraroqoF Ha MEo)litrHi M' Po3r']IflEcl1o r, > r,

1o8. 1) 18a3 =

€M 1o2.Hexan.i.r '-

r'l ,r""r= tr.,) c(r,) l(j.,) s(.t,) .:0, ro6ro v(x,) '' l/('r) or'{e' ,,i r.'."vri r''' s{'' rpo" rrovoumter{u 'oH'Ho\r'Hr '1I 103. Hanpntraa: OvHRqin ir(jr) = xtr(r' 2) lle € 3poc Ilcxari /(r) =

i s(r) = x

'{aMH(,itrHi[0; HP. 3pocrdn,orrl

q]vHRiris,(:n)

a-re

nad' aH1

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qlrx qrcen € Han6inEurM, r\e 'rtrcro 2) Po3r,lflEeMo drvlrrirrilo tlilioM qi€i

vtsllqi;

napa6ora,

a)i, v =

y,=2 16-16 4+64= 32+64=32' qlrc'{o32

HaiiMeH Irlt 3HaqeHIt'M cvMl'

riBaApariB 3aaallnx qIrcer.

200 \' B ABt 20o AD AB 100. h'x"t AD :(' rcn ,r,a = IOO ,. 'S,,,",,='(10o .I)=100:r a! Po3tnflEeMoOvHrpaoi(oM e rapa6o'1a' (Bir(s' Enoi Ea nqiro ri = 100r Il 100 '1" ro u 50nu 2500 2i00 A npFv rF dH/J. * qt'c'Io 2500 € naii6i'1!ue 3IIaqerIIr€ OvH(qii v = 100ir - ir:' roMv Eaii6i'1!Il]a ltroultr

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+ =;;

2) r18a):= 18 : \ \ ail =( 3)r=9i

( 2f= 76+ 4=20;

4) (16 +

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(

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+ b'>a'b+ ab'

3)(-12)'<(

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112. y = l(r') € rapEoir, ro6ro

/( r)=flr),ronii

1) f(2') - f(-2\ = f(2\ l(2) = 0, roMy piBFicrB f(2) f( 2) = 1 Henpar nbHa. 2) piBHicrr, l(5) l( 5) = 2 llerpaBr.,rblIa, 3tsa.Iel{Fn l(5) = l(-5), 6i) rDyHX4n a

ro!) ro6l-ox ' 'rrri " a"arr e. | /l l) /' ' ' ,. ,,*, ,:,-:"." /r | |

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aopiBEllr€ 2500 M'.

106. AaHo f(x) = 1:, r. e R. r" rogi O)' Hexan r., € (--; 01, x, e t0: +-)' roai r,:-'rc' ftqo ,x'l ': ""'i L!'' Jro6rr (1r i {2r^arctt -:lllal:T (2) vMobf < :ri > ro,ri sErqo lr.;l tr,l, 'i Ir'' i ' oBoK. Llu /i') r H' ' H Jpo'aao 'oro " 'JHo''

254

l .:

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napHr.

a'+64 76a+a'1=2A' 16.,+64- fpa 16 (!ir(u"l{oi EarpEMjlesi Bropv' a x' = : = 4'

v = a: + (8

0.; 2'o 0.5 .2 0,5

= (a b)la b)la t b) = (a b)'(a t b). Bnpa3 (o ,)r(o+t) >0, ocd,'r!l{na'0, b > 0,,tor{y ar s'r6!a epiBrriclr,.

()610

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2. napHi i HenapHi OyHKqii

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ll.nDU{ir{{tsvI0; _3 - 14J""' iai'(rlc

0,5

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spocraloqi OvE1rqii

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36-'6 6-6'0,,c

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I 15. 1)

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3)x€[6;

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IIe Mo'i{Ha

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= (3x 1-1)'* --L(3x +

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'o'v '"f"" il it,l= s,^,te R:f( x\= 5 ( OyHlrrrielo Ha

= 5'{- l(r)

/:_l

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r.. i.-.--.-..-.. ::til].ai:L.:.!:

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=rrjr) or'j{e -21o (-2i

e napHol(,

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Or*{e, cpyllxrria f\)d uiaEocEo roqr$r 0.

= -: 'l-t

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t:=-I \x'

naprolo Ea c'MerpnqEiii Msoxxrli

[-1i

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(-*i +*)

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. 3t.

a) l(')

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Syt{Ktlis

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(.'6; *

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256

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runrgspa Mep3ncK A. f. ra iH' AKaaeMi'{H}ri piBeHb

l,l..,l;,.r,

[--,-;)"1

= 4r:i, o6nacrE BrssaqesEs: xe Rif(-rc\-4.( r\1 = 4x1 = -f(:(). € Henapsolir QyHI{qi€Io Ea Mso'{aHi (-€; +@), crMerpuqHiri BiaHocHo

l(r)

sQO

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ct-i=J, e,) J,+t xt=rZ;-rZ:; =,( ,E*r*"E-)=

Orr{e, g(}) € EenapHoro OyEEaiero Ha MHolrrsi

117. 1) l(:r) = r", n € N, n - napse, jr € R. Mllo]*inHi fl-ir) = (-r)" jr' - l('), l(') e naptlolo OvEnqi€Io sa cl'Merpsqsifi

-(3x lj-

4l f(') = (5 r.)5 (5 +')' = (5 - ('))" (5 + (,))' = (5 + r)5 - (5 - x)5 = = ((5 r)' (5 + r)'?) = -l(r). Or,rc, l(t) € HenapHoro OyH(rdeb Ha MHor{trEi ( @; +@), cxMerprqlliii BirirocEo

6r nrr . rx , 2tx 4 lr 2,l' t 4, o6narrb Brs"aqeHHs Ovlt(uii: { -: -): 7-,, ,-t zr-, 4 -l x-2) r 4! -lr 2t) -4 t tx 2tx a - ftx\' 4tx'4t tehoto.,qo a = d. roM) x-4t x 4"! sa clrMerp{'rHifi MHo'lrclxi ( -; +-) BiasocHo roc' e napriolo drxe,

l(r)

( r)E = 2r.+3f = (2t - 3x5)= -f(xj. 2) fla)=2x 3r3,re Rif( r)=2.(-r)-3 Orxe, flr) e nelapHorc ibysliqi€Io Ha Mnonirlri ( *; +-), crMerpurrHiri liAHocr]o ro,llrr 0. 3J fe) = xx), r. € nj l( r) = (-')l-'l = rr.l = l(ir). Orr{e, flr) e HalrapBolo Oyllnrri€Io l1a MHor{rlri ( @; +€), cEMerprr{Hiii BlAHocHo

'ndpts.ro

u (2; +-)'

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flr) - napHa Oyrnqis sa Mso,(r{Hi clMerpuvHiri BiAHocno roqKr.r 0. Or,{e,

/(r) r'-aI

1)'

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l i -L ''--i. ,,',= il-r.l,i -; : MI'oxsIIi ( *i

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l tur {3r --L-- ll' t3"r-lt

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g(J.) a seflapsoro OyFriqiero Ha MHonirHi

[ 2; 2],

( -; +-), crMerprqEin

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e(j')=r",r€ N, n

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lt ll

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x'J"

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122, a) IapHa

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f(x)

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125.f(r\="-4awvr>o. 1) l(') - rapEa;

s( x\= f(xl - s(').

@Frrcqis y =

l(')

a) s(-:t\= fG) +s(r). @yE&qisJ=l(,r+ e(t)=

r\. ( s('D=-^r).s(r)-

€(r) re s(r') se

y(,). oyHKr{is

134.@tErcaiifigB

126, a =

f@)= o,sf , r e LOt 2li flx)=-:,

\ aQ\

!>2.

2) g(js)

rapEa;

3saqeEi Ea MHonirHi n4, /ig - ueDapEi OyHrqii, rc6ro l(-r) = -/(r) ig(-r) = g(jr). Iorpi6Ho aocriarrn sa napEicrb OyEftrrilo: 1) a=f@)+ s\t\, vtr., = f(-,) + e( r)=-flx)- c@) = (l(r) +s(,))= y(r). @ysriqis y = l(r) + g(r) lretraptra. 2) a=f@) s(rr, y(-x.\ =- fl-x) c( Jd)=-l(r)+s(')= (flju) €(r)) = -y(r). @yEKais a = flx\ €(r) - EerapEa. it)=-flr). (-e@D=f(r). 3t s = f(x). s(x\, vttcl = fFr',.c( s(r) = y(r)..DyHXrru ,=l(r).s(r)-napEa. 135. / ig - seDapui, ro6ro /(-,rt ftxl, gFxt = g{xt i npr aboMy OyHnurt hIt'l - -3safrAeMo ft(-.r). elxt fl-tl fttt ttrt ht x) . = -- = . gt xt gr.r r g{,r) lr-r). oyHKtris ir(.r) e napHoro.

EerapHa.

136.

127. /(r)

Eerapsa OyEnqiF, 0 €

ft!) Heuapua S! Hxuis. BoHa nae 4 Hyti. AoBeaeMo, nro 0 e D(r. flpmrycrxMo, ro 0 e D(n, roAi l(0) = 0' ro6ro OvHXqin 4. MaeMo npornpiqqs. Ort*e' 0-€ ,(r. Bnie Ma€ 5 HyniB, s aa yMoBoro

12A.

Ma€ 7 Hy'rie. - HenapHa oyHKtrifl i € crMerpnqEa Msox{LIHa BiAsoctro ro'rKIt 0, lra

,(f)

sxiii

Br3sa'resa OvHKqin

l(t)'

l(0) = 0. Mae 7 sy"ris, to,ci f(0) = 0, 60 D(D € crMerp"qna MIIo13O. flx) - napEa.byHKqin i ,rinEa BiAHocHo oci Oy, Aa Eftii Blr3Hs.resa abyHRqis l(t).

orMerplrqHa MAo*{ssa Bi,qEoeHo toqarKv RoopAl-rlrar (o6nacrb 131. 3a yMoBor M r), roAi g( ir) = l(-r) + l(r) = s(x), ro6ro BEBHe.rel{Hs OyF&qii r, e@) = f(x\ +

EG)

rapEa OyHHuifl,

Iloqar&y l(oopAr'Illar (ofulacrb Br33a ylaosoo M - cnuerprqlra MHou{ItEs BiAEocno f(-x\\' rla'reEEs Oygxrrii n, h@) = fixl - f(-t\, roai ,(-x) = l(-;r) tQ, = -( t) HenapEa lbysKqin ro6ro t( = -t(t). oril(e, n(r)

132.3awoBoo I ig trapHi lbyEnqis lla MHoE{I'IEi M, ro6ro l(-t) = f(') is(-t)= g(a). florpi6Ho aocniarrr tra napHi.rb SyHHqiIo: l\ v = f@) + s(t\, aC t) = l(') + €(-t) = l(ir) + s(n, = 9(r). ovnKl{in I = f tx I + e(x, [apHa.

2\ s=f(x)- sXt),v( r)-

-x)-c, t)=

x) -s(t)=y(a). (D]'El{qiss=

x)-s\x\-

rIapEa.

260 iJi AnTEEPA Mep3reK A, r. ra iH. axaAeMiqHnr

piaexu

ill{liiNi'i:li;I

lbt

EKqiI, oAEa

srclrx napna, a

Apyra

seflapua. <lyrrrrris

h(i = 19)

g(-x) = s(r), roMv r'apHa, ro l( a\ = f(xl, a s - rieraprra, ro fGt\ ftrt ftrt hFxl. . . et-xl sltl strt flKqo l- s€trapEa, ro fl-r') = f(r), ag- napEa, ros( r) = €i(J.), roMy .. lJ ft xl ftrt 'ftxt ' h( ,(r.). OyHxuir lt-rt HenapHa. .- = c( .r.) -c(.r) eG'J flErqo

l(f), rouv l(0) = 0.

129. I\x)

Iig

137. @yEX4is / BnBHaqeEa Ha MEonirEi fi. 1) Hanpuftirag: y = a3 - Henapsa Oyl{ftqiF fi Ea MHoxcrHi rg 3pocra€, ocdnr,xr An! t"2> x) (tt e Rl, aG,, - a@) = > o, rc6rc > uQ). '3, tOyunEis fi Ha v@,) 2\ Hanpve'nlat y = '4x HenapHa MAorrrBHi R cna{a6. 3) flpulrnaa seBecrr.r He Monitla, 60.anqo ibyHriqis rapEa, ro ii rpaoix c[Merpr.qssii BiariocEo oci OV, roMy Ha oAsifi riAMHor{rrHi QyHprqin spocra€, a Ha iHrrii craAa€, i IIaBnaKn (sa yMoBs, qo o6nacrr, Br3naqe[Hs cxMerpr-rqHa MnoxuHa siAHocEo sy.ns). 138. I rapEa OyE&rris, .sna spocra€ sa npoMix{i{y [0; +-), roAi na npoMir{(y roHa e ctranHoro, 60 rpaoiK O).Hriqii cuMerpr.rEnii BiAEo$ro oci Oy. HaDpuRnani lJ = t2: y = x).

139.1Ipaoix Miliiliy

( -;

HetrapEa OyHlrrtis, BlrsHaceHa na MHoxr{Fi R, spocra€ Ha trpoMt(Ry [0; +-). EetrapHoi Oys&qii crMerpraqHrfi Bi{Hocno noqarlly KoopAt Ear, roMy ii Ea xpo,

( -; 0l qs dyEl{qis spocra€. Hanpxknaq: o=L, o'oro t".

i:ii:;liilliil:it: AnTEEPA MepsnrK a. r. ra iH. AKaaeMi,{Hrr pieexr

:ii!:

261

14o.J napHa.byE'iqis. Tlli{.v) 2. TqI /l'rl 5. oc,(iiLHx/- napsa OvHHui', ii rpaoiK cl,verpfiqHri EiasocEo oci 9. rovy ,minrllx) 2. rnsx /(r) = 5. I e senapnoro i nti'll(xl = 1' maxfla) = 3. Oc(inbKr'r f(x) - HerapEa Oynriqin, ro ii ryaoin clrMerpr'qHri BiAHocHo roqarKv rioopAl{nar! roMy min l(') = -3, maxl(r)= 1. l-3: -2) I-i: 2)

141. Oyr&qi'I

BnPaE'l Anc noaropeHHt

u 7x 3, l{ 3*?-" (l), l" l"" ll 6xs. y s, I.r - 6113 I 7xt-tB 1xt'z=9

:i:t:.:.:.:i.I.

tzt.

Bi.)no.)idb:

u-. Bt

Y = 6;

(gi-t): { li 9t. 15.

l['-r' 'fr t

'0.

,' l['= '' JP'=18: = e. = lL2,

15.H"*u,;, tu=a.rc

[x-u-rv "r[,tv',0= x'zu + xu - 54t ltvk ' u\ = -54' l, r b = -15. ]d -15. b. rlr(2r. It'" 54: lrr l5 bt = -54

I'o3B rlKeMo rxcreMy piBHflkb:

fo t' i6

'o'

[u, r-',

1,,\

22,

60u,

l. ro '

\=22-D,, 661 22 D, u, = 10

1320 + 60u"

r:l)-

- 22v" + o: =

u" + O, L),+ 22.

x2+l8r+4212 g 42x- 4g!'=9; -6t2 24a- 18=0; t'+4t+3=0;''= a6o x = -1. flxrqo jr = -3, ro 3/ = 3 - 21 = 18. ffxqo jr= 1,roy=3 7=-4. Bidnosidb: t B: _18)i I t: -4). l*_q=ro. lfz* = re. l[* = g. , ar ]lzs = -2. ly = -r, ,, Jt - u, 2r! too. atx vl - roo. ] ' ir

'' ly,, s,

/r sa I ror. 6

60tl, 60(?2 p,) p,(22 D,(22 - D,)

PoaB'rJ*{eMo piBEnl{Hn (2):

a-.:.t:.:'tt

PGB'.'xeMo piBEnnEs (3):

142.1t ':'

'.4:i

xB. I 60 -6^ l.l .oa.: s 66 t=;-'66 66 66 ll 6 6 I - ra ^ '=t=t' u, ,-', l0i u ,, t0{r) lp{ roarHh Bonh opo lxaru 66 HM, ro6ro 3D1 + 3u, = 66; \+D,=22(2')i t> 0, I,j >0, u,> 0.

143.3d )voBoo

[1!/

o +98a -1320=0; .D -qg' 4 D,

PorB exeMo piBEflHHt l2r:

- b, = 54i b' + L'b 54=Ot D = 225 - 4.1. (-541= 223 + 216 = 44li 2l -ls{ A "t22-"'z22-6 r, a =_15-2I=_!9 t8. g$rqobr=3,roa,= 15-3= 18; sRrco b,= 18, roa,= 15+18=3. (3r 1r ]x ' = -ls lx -I8 e (a). po3s sxeMo piBHnsss r4r: y)y 18 3 3: = lxs L( ,18v y,=3,a,+18y+3=0; 2=sr-s=zg, y,=-o-.fia; y"= -g+rte,

3721, J3721 6tl

= -49 + 61= 12.

r,, =

-49 6l=

14O-

BpaxoBymqr yMoBy ,, > 0, MaeMo u2= 12, ro4l Dt= BidnoqiAb: 10 F"Lr/roa.; 12 r.M/!oA.

12 = 10.

3. no6yAoEa rpaoiKiE OyflKqit 3a AonoMororo reoMerpreHnx nepeTBopeHb

144"AarJoV=t'.

2)v=Q

1)a=x'+5; 4Ju=(x+6\';

.lSzo 24ottl32o

a)'i

5)y=(.Y-g):-2i

145. BiAnosiAb: 4) y =

146. BiAnoqiAb: 1) a =

f + S.

3)a=z'

10t

6)r=(r+1)'z+1.

4\2.

147, BiAnMiAb: 3\ Ea 8 oanHr.rrlb rpaBopyq.

15b

roai

'' =-18 (-o-.fa)=

s+.,,Fs;

,,=-rs-( s*"8 )= g

.,88.

,-.,fis), (g '[s;-s*'q8). 3 - s' x + a = 3' {51 poc" pi""',r' (o), 2t [x '*.'o l'y = -rA: l{3 ,)y = 18 {6). 3 t s t2 3u-y"= \8; y" 3y 18=0;r=9 4 {-18)=9+72=81t u.=;=;=61 t-n=j 3. rori .r, 3 6=-3..r, 3 {-3) 3 3=6 ," "22 (-3; (6; 3). 9), Orxe, Biono iob: (-3i 6), (6; 3); (-e+,fi8;-o-'fte), (-o -.,fia; o*.4a).

148, BiAnoqfib: 4) Ha 3 o4HElrEi niBopr,.

149. a = fl;r).

1\y=f(xr-2; 2\a-f@r+4; 3)y=f(r-3ri 4\a=fk+1\; 5) a =

-fl'');

6)a=3

f(r).

orxe, [-o + .,Fa;

262

:::::::

AnrEEPA Mep3nek A. f. ra iH. aKaaeMiqHnr pieeHb :ii:::iii:i:::.ii:i::i

:ittiitliillii:

AITEEPA Mep3rrx A. r. ra iH. aKaaeMi,{Hnr pieexu

i{li

263

Pxc.6

1)a=fQ) 2; 2)a=f(r)+4i 3ry=f(r 3\. 4)v=f(t+t); 5\ a = -f(r\: 6)r/=3-l(')

:.-:if il:]: I i ::t.:.!:i.

154. ArropnrM ro6yaoBr .paoilla OyErirrii:

rl a=nE-+:

a) 6yay€Mo rpagill dryHllrrii y = G; 6) ryaOiK Oygrllrii v = G ""p"""""*o "u pajr€nr,Eo IIa 4 oAnHrlqi lHra.

2\ lJ=n64: a) 6y.qyeMo rps$iK OyHKrrii y = Ja; 6) rapanenbHo nepeseceMo qefi rpaoiR Ila 4 oArlrnqi npaBopyq.

3) 151.

y=G;+3.

Cflo.rarKy 6yny€Mo rpaoin OyHnqii y = G. noriM noro nepeEocrMo napanerBFo Ha 1 oanfl}rqlo rpaBopy.r. OaeprKrMo rpaoiK OyHKriii , = \fr i. noriM qefi rpaoiE nepeHocr.rMo napanenl,Ho Ha 3 o4aHllrri Bropy.

155, 1) y = ?;

2) Y=1 lt

= l-;

4r u= - +6. flHqo ryadliH Oynllrri.i 2

napanenbHo

ncpprrcrTfl sa flr<u{o

o.trxH qro BHrrJ.

6ttvt" y ? 1 '2r. repeHecrr Ha I oArHrrlro ,'riBopyq,

ro onnpy.'{Mo rpa$ik

fpaoi( OysKr{ir y = a rspanenbHo xc

oAeDxlvo rpaoir oyHl. (ii 9 r-tl3). glrqo rpaoir{ OyHEqii , = ? tup-"rr""o ,r"Oesecrl sa 3 oAuHuqi npaBopl r, a troriM Ha 6

264

i:::l

A'|EEPA Mep3nrK A. r. ra

iE. AKaAeMi,{Br'tr

pieext

il::iliiiiiiill:i

oaxHru6 vroD\, 1o orepvHvo rpaoiK O)HKuii,

iiiliiiilittiii

='--.--6

{4r.

AITEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hnr piBeHb ::::::: 265

156.l\

!/ =

x'1

2)a= r'z+6x 6;y= (j.' 6n+9)+3;

4x + 6;

y= (r'

g=A' 4r+4)+2l a=(r 2)"+2i

3)'?+ s;

1s8. 1r

,, 4'rtl 14 4{irrrll) -lO = 4, l0 .r,l'

jl:

- x2 (t 2)s ): 2

12 -

7) 5

r-2

, ,l:!: jl.:

3)A=2a'!-4r+5i

=2(:t' 2t+t)+3, a-2(, 1)2+3: 4) u = O,2x' 2x 1; y = 0,2(r'? 10r + 25) v = 0,2(r 5)r - 9. a

3r+8

157.1) y=-=3',

159.

Io6yaoBa rpaQilla OyEtcqii

8 ,

,, ,, 2r-'14 2t! Jt I 'tc x'3 3 ' 2t 2t\ lt ,. xt -''rIrLI

g= 2-'

-2, r 3'

a) 6yayeuo

.. y= 2 ;

,._,

6) 6yAyeMo

r= j;

161.1) s = 0,5aF; D lt = -z"E:Z.

2 2

=o,b

v= ,_t: 2 r) 6yAyeMo != 2 , I.

B) 6yAy€Mo

266 l::i A'fEEPA

Mep3rst< a, f. ra iH' AKaaeMi'{Hxi piEeHb :::::i::::::1t::::::::

i'.:*ii:1:il:lil:ii: UfeSPA Mep3neK A. f. ra iH. AKaAeMi.{Hrt piBeHb

i::*

267

164. 1)

Bianoaiah:2.

BiAna6iAb:4.

169"

167. 1)

BiAnt)6iAb:2.

BnpaB14

171-Hexan r rpE.

Ar9 noBropeHHe

qiHa roBapy. fliABrqeHa qiEa roBapy

t + 0,25x = 1,25r ryn. Ma€Mo: 1,25r rpE. 100 %; r !pE. ! 100 a l0 0OO -u 1.2tu 125 80: l0O l, -80 A =2lak. HoBy qiHy roBapy rpe6a 3I{]IsIlrr Ha 20 % Bidnoatdb: Ba 20 rl .

"/";

172, I]icnn BrraposyBaHns 3anrnrr,rocs 200 40 = 160 (r) po3qrHy. y 200 r pos.Lr Hy Micrnrbcs 8 % coni, ro6ro 200:100 8= 16(r). y 160 r po3.rrHy MicrrrEcs I

BiAno6iAb:

268

.oni

::::i:;:::::ii::::::iil:i:

t6.too%

To6rn

BiAnoRiA,: 10

l::l: AITEEPA Mep3fleK A. f. ra iH. Ar<aAeMieHnn piBeHb

fi r

160 .

-=toi,Mep3rqK A. f. ra iH. AKaaeMieHrt piBeHh fiitiil{li::.::.::J AITEEPA

!ii:

269

t 173. Hexan v roqar$oBoMv crl,'laBi (12 +

t lir qrlrxy,

Kr. -Biacor&oBLIE BMicr Irllrrny

crra;i crag.t"tt ', 100 . 12+ x (12 + tc + 2, = (14 + jr) I(r. BiacorKoBr'di (2

BMlcr qIrHIly B EoBoMy cntaBr cl{naAa€

lr'Rv

Mat Mo

3(8+

B HoBoMv

"o,uui

r.r)

al33" = 4

x) 100 r. 100

12 r

PIBH'HH': J4

","

- x -.a

Ei:.i:.:

i,:i#:i::..i it:i1l::l:::

100 oo

124' 12xltl2-xl-12xtl4t

1168 | l4x I

12;

l6At - 12r' -

3(14+'X12+r)

x'-26x-tzl 3tl4 rr.)(12'.r)

12+r 3'

74+ x _ 0.

l2x x'l 14r.

l2r I

=0j

a ra rracrrEa,

Hrli.re oci Or, uiri o.i.

-4

z-,

r.?

BiAo6pa-

}Hacrb.s cIrMFrpxqHo BiAHocHo

D t69-120=289, x' - 26x 120 o, 4

13+17=4.x,=-13-L7=

BiAnosiAb:

176. Anrop rM ro6yAoBr'. 1) y = lG);

2) v = f(b) vacruaa rpagiRa OyllKriii l(ir), s&a ,!e){Crr6 trpaBopl r BiA oci y (i Ha caMin oci), 3anr.r uacl6cr 6er rMiH r BiAo6palHacrbcfl .IrMFrpr.r.rso BiAHocHo oci Oy; 3) qacrrHa rpaoilta OyEKrrii u = f@l), axa, rcxe]lTs Brqe oci Ot (i Ha caMifi oci),3an[ aerbcs 6e3 sMi1i,

^ l[x -26x-]20=0, (,: (14 x){l2.ir), 0.

Po3B s,l{eMo piBHflHHr I

16A =

iJa yMoBoIo BrAcorHoBtt

(2+!\'4

3\14-x')l12tx) 288 + 24x: + 144t +

2. lpaon{ y = lflr)l 6vAy€rBcs raR: ra r{acrrEa rpa&iKa OyHKrrii y = flJ.), sria,'lexcrrE Bnqe oci Or (i lla caMin oci), saimrra€rr,c.s 6e3 3MiE, a sRa rer$,ii6 Hrxr.re oci Oir, BiAo6paxa€rLcF crMerp*iqso BiAHocHo rli€f oci.

6iftmsii, rrr{ y Doqarr{o3oMy.

4rX12+r) 3 4jr(14+')-(14+')(12+') 3(14+r)(12+r)

ir't

roqarxoBoMy"

SararEra Maaa HoBoro cEna3y cl(,'lana€

sMicr

3al'anbHa Maca rlEoro crlraBy

30,t=4 BianoBiaa€ yMoBi 3ana'd. rrosa'rxoBoMy cflnaBi 6yno 4 &r q!,rrrcy.

177

ForyeMocr Ao BllBqeHHg HoBolreMx 7: 3A=r+7it:=3! "3 ro 10 10 I0 2\'=" t 2 t tt: '" tt x-2 : t-2=-t .Y 6 t u 6 t2lx/,li r:--= tStgtll Lx+2: fry'5"5u*--'=tr g-t=!-'": 25(y +1\'=r.+2. x=25(u + 1)' 2(r> 2,y> 1r; I I 1 --=1 I 1 I a-. 1 c-o-i b=- I o. 4l

174.1)

'a --=-: h c

(a+O,b+0,c -O,a+c).

b - ac

fia.\ a=lx'

a=)G-zl

Konu 3po6neHo ypoKl,t

'175. 1. rpaoiK y = l(t) 6yay€r6cs raR: ra.racrlrHa rpaoiKa Ot'EKqii y = l(r), sfta ne)Icr-rrL rpaBopy.r Bia oci oy (i Ha caMifi oci), sa-'lsllla€rbcs 6e3 3MiII i Biao6p&r€€rr, cn cnMerp[.rHo BiAnocno oci Oy.

n, "

"=ll'-t"

27o

it;:t::.

,.IIIEEPA Mep3neK A. r, ra iH. A(aAeMi.rHrr pleenr :iii:i:i:iii:i:i:i:i:ii

:it::iitili::ilitl ATTEEPA MepsnrKA. r. ra

iH.

AKaaeMi'{Hrr piBeHb

li::it

271

f Airopl-rrM no6y4oBlr rpaoina OlBlrrii y

3, v=,tE-rl+2.

fpaOiJr Oygns,ii lt =

2\ a== 3)

=':XL I

,1, tl , 2

clrMprpvqHxfi

Bi.qIIocEonp€Moit=1.

1 (Dapanenhflo nepeEe.eMo BHt{3 Ha oalrnxuo)i

=la -1 t.{acrrrEa rpasira OyEXuii. sl{a ne}rnrr,

sanrma€rbcs

Bnlqe oci Ox a6o Ha oci O.r,

6e3 3Mif, a ra qacrrtsa,

i Ot,

BiAo6par{a€rr'cs

criMerpnqno BiAHocHo oci Ot).

179.1ra=@ t)'i

4)'- u = --=_. ix+11

.1 " .r+1

l Dadrk rhvHknl

crMerpr.rHz

BiAsocHo npnMoi

-1.

=',Ei;

Itijh:Uf::i )i::c+!!:.1

i,:i; .llt:

4, O6epfleHa OyHKqit 181, a), B)

roMy u]o

MolrcHa oaEosnaqHo Bnpasr{rs qepe3

y sa o6nacri sIIaqeIIl,

3anhsoi oyEKqii.

lA2, a), 6), qa,qaHoi

roMy rrlo

MoniEa oAEossaqEo Bspa3nrl-r qepes y Ea o6nacri sEaqeEb

oyr$cqii.

qepes A = l, , , e n, y € [0; +-). OcFiinErc.r r Ee Mo]Krra oAHo3Eeqso Blrpasltr]r v Ea o6nacri 3EaqeEr, sa,qanoi abysxqii, ro Aana OyEnr\is fle e o6oporEo1o (Hanpu-

1A3. D

&''.aA,V=2,ax=-2it=2). I 2) u=+, xe (-*;0) u (0; 1-1,

g e (0; +-). OcKinr,RrI, Ee Mo*clra oAIioBEaqHo

Bnpa3rrrr qepe3 y sa o6nacri sHa.reHb sa,qasoi O}.Ir&Irii, ro Aalra Oylrriqis Ee € 060PorHolo (1lallprRra.q, Y = 1, a t = i:1). 3\ a = 5, r e R, v e l5l, Octiinbr r t He MolrcHa oasosrraqtro Bllpa3rrlr qepes y Ha o6nacri snaqellr, Ba,qasoi OyHftrrii, ro Oys(qis y = 5 Ee e o6oporlroF (I{anpuKnan, I s. a .r = 0. 11 ra iHroi).

rso. 1) y=r/r+21;

2Jy=(lx-2-1)"

184.1)!=3x: 1,xe R,3x=V +1; t=g-!, ge RlDlxl=r(y,t. nosHaqlaMo B oAepniaEiii OopMy,rd apryMeEr qepes t, a ibyHKqiro .rep$ y. MaeMo OyHXqirc 11 s==x -, sl{a. o6epHeHoro ao OyHHrii, = 3i l. 2t

1 1, x e (--; tt

u (0; +-.). OcnirE(Ir

Ktrifl o6oporHa. 10 Bl4paxa€Mo.r

272 ',:* NllEEPAMep3ncK A, r. ra iH. AKaaeMi,{Hrr

pieenr'

lll:ill{ili:iii:i

qepe

Bcii o6nacri Br3HarreHss

AaHa abya'

yr ( @i 0lu(Ui i-1.

i:iii:,1!{iilliii LnrEsPA Mep3rrl< A. r. ra iH. AKaaeMirHrr

piBeHb

.allj 273

f SMiHroroqrr no3Ha.reHHs Ha

at u=

rpaArqirlHi, oAepniyeMo

IIs OyH(qis

o6epHer$

Kqir o6oporna, ocllinr,Kr s lirnrrrrro y = !

MoxHa oAso3HaqHo Bupa3xrx .r

9C92!'

rpa,qaLlifin.,

t"'

!' ,ur rDyHK(ir.

o6ppHeHoo

R. I{a

sciii o6nscri OytsRuir o6oporHa. 60

Mor{Ea oAHGrravHo Br.rpa3urrI

qepe3

,qxuiiiHo:|] =3x .12.t\e SyHKrir.

186.

Il u=-L. r+ l, r e (--;

oc&in6xE

piBH.sHHs

---:-:

piBHrHHfl

y: v= g-4:.x=3c-

o6epHeHorc

n."**"".

tpa.qlqiiino:

r. Orr#.

yMoBoror(y) = [2j +*), roai y 2 0. 3 piBEocri s = lFJ MaeMo. t2= y!-t 4; r=!,f}i, ane.!€ [2; r-1, nou"us'=i 'o-y '=.,[t*a. .ra€Mo rpaAxqiiiHo: U=.lF+4 Q>O,:(>21. qs dlytlRrris o6€pHeHa Ao Aauoi.

r'i

6icenrprr$r l.

2) @yHKrrie !,(r) o6epBeEa ao OyHRqii y(t). fpaoi"t OyHXqifi cuMerplqEi BiAHocHo 6icexrprcr l.

o6nacri Oyrxqis o6oporHa,

Brpa3rrr jr

MoxHa oaHosHar{Eo

OyHRuis o6epH"r"

r=].

12. Iloosaqrr,{o rpa-

ao.byirxuii n j-

u (l; +-). Ha Bcii

O.Ma.Mo

s ] "".*., ri$=r, vr

3, a = 'lr"-.3a

BiAEocHo

tl U ;x t 4. r r

188. 1) (DyHKait yt(r) o6epHeEa Ao OyEtlqii V(r). rpaoiKn OyHnqir; cxMerpr.r.rHi

!o OyHKuir

" z'-l At

yuoBo,o

o.spiBHo.ri

orxe,2r-1=1, z,=!.'t, zr=!'u, r=t e,,,,o. Mo

qora

rr ' U. y l,t. Ur

.rep$ g (y + 0 Ha o6nacri 3naq€Ilb 3a.qaEoi OyHRqiI).

nosua,r

z,c I. x 0.ro,ais ./r-Jra ItpaxoByroqx.

).. Hasci;o6.1a.rioy -.;)1l ,ll;, *J.

2x-r.0.'=;.'.1,

it.

qepe3 g.

!(r -

1) = .r.

! .. g, l.

gx c x, yr r = U. xtg 1t = g. , norHaquMo rpa{ruiiHo: vt.. , r l. olpuvatMo oyHK(r'o. ooepseHy,4o aaHor. . 2ta J2x 1,2! lzO, x,:, r Dtcl [r l;t r-1. Ha rriii o6nacri.r MolxHa oaHo. 2z qepe3 y. Bpaxoryrcqr, rqo y > 0, Ma€Moi y2 = 2a 1;2t = g' + 7i 3HaqEo Bnpa3xrn ,

r=?. no3Ha,r,rMo I{uii y J2jr l.

rpanuuifiHo:

3)C=2Jx t, r > 0, r

e [0j +-), y €

u=--

[ y).3AaHoi piBsocri Maer'ro: y+l=2./r, 1-I onepxrfMor (y I ll: - 4r. x-'llJtlf.

- ur ibyHxrIfl o6ep:rera

BiAsoc[o 6iceErprcr l.

4o rblr.

1;0) (r oaHo3Ha'{ao Mo}rcna Brrpasr.rrr.r qcpej Bpaxosyror .r yMoBy, + I >0,ro6roy:-1. nosHaquMo

rpanhqiiHo: g=

Otx

rlf.

o,qeplttvMo Oy,rKrilo. o6epHeHy Ao AaHor.

qu=r!,D(yr=( -;01, roAiy > 0.3 piBEocri g/ =r? rpn y > 0 orepxyeuo r = tJg. BpaxoByroqr, qo 3a yMoBoo r € ( *; ol, Ma€M. r = -u[. n*"rr**o rpaa'qiiiEo: y = -G. U" Qysxqis o6epHena ao aarioi, srca 3a,qaga rirbnr Ans, € ( *; Ol. ft7., y=!12, r€ ( *; 0) ..-l (O; +-). Octinlnr r oaHGHaqHo qFpF3y.roirr x 2, ux x -2.xtu ll=2. x=:t,g-1. Ilo3EaqaeMo

(DyHkuir ,,(rJ o6FpHeHa 3) g = 1_ lzx, t < u. ao OynKrrii y(r), ixHi rpaoiKn cniBtranarorb, FRUro.f,:0: a flKuo.r' 0. BoHu CrMeTphqHi

rpaArqifiro ii orprrru"*o: y = _f

1), = 3t - 1. @yHXIti.s yr(t) o6epneEa Ao QyERqii y = 3r - I, ixsi rpa, Oixu cuMerprqsi riAHocEo 6icexrplrcq

149.

I i III r.oopansarr[x KvriB.

2\ v = r' - t. oyHxaifl y,(r) o6epHeHa Ao OyHKqii U = )c' - 4. IxHi rpaoit{Ir c[MerprrrHi BiAsocro 6icerirp cr{ I i III KoopAuHarssx nyriB.

Moxlga B'pasrlrn

Lls iDyElcqifl o6epse!.a ao aanoi.

274 ii:i AIrEEPA

Mep3nsK A. f. ra iH. AKaAeMi,{H}ri piBeHb ::i,;i::i:li:!:i;:i!:::

i::::illiiiit::ii: AITEEPA Mep3rsKA. r. ra iH- AKaAeMiqHy.y. pi*e{h

r* 27i

["G. " y=lr

lt.r.

195. Hexan 1

.r < 0.

po6ora, roni

rep

.Jr 3 ro,{r{sl-r loHa nanoBHro€

Ipa@ixu o6epaerrx OyHriqifi v(r) i yr(r) ctr, Merprr.rHi Bi,qEocHo 6icekrprcr I i III KoopAn-

ranonsur{ f -

i =i

a rpy6a 3a g roAlrH HatroBlrne

rrI :933 =:

o6'€My 6aceiiHa.

]

oo euy oacenna,

Apyriii rpy6i 3arlrllrnrloca

06 eMy. BiaoMo, rqo apyra rpy6a EanoBnlo€ 6aceiiH sa 12 ro-

o6'cuy eona 1;oo,;v 'anoa,r,rtr ".r" ","""",rr I ooc'y,, I I rz s 1"oo,u1.su"",loovie'"a,,o",,""o"lt*t=11 (,oaxnr'

nHH, roAi 3a

1,+-

.,^

B;dno6idb: ra

roA!,t}l.

196. Hexafi Apyra 6pBraAa Mo]rte sopar,r rone

rlroqa) sa J' roArE, roni rep-

3a (, + 12) roar.rE. 3a 1 ro,qnHy.qpyra 6pErara MoJ*ie Boparlr !, u ,r"p*" str l2' * 9* ToAi pa'oM Ba l roar'y BoH' Mo,{yrr, 3oparr, 12! "r - = "t1 ' ir(x.'.1]) 12) = "\'. x r'12 "r(r+12) s(i* *,ll) ro6ro sa 8 roalrH. pasoM BoH' Molriyrb sopa'r 3a s , rrJa

vce none MacMo

191, IpaOiKI, o6epEeHrx rbyHr{qin y(r) i y,(r) crMerprr.rEi BiAEocEo 6iceB

x(x + 12\ "oaoo,

DiB,,EHr': s, '

2sl' *-9.1 -- e, r(r I 12) I 2(r 6) x(x - t2)

+2r=16' + 96; r*

x'z+2r-L6x-96=O: r'

'2 ! 12 a6o x 8. 3a 7 roArH vot+re soparlr nonc Apyra s.\ 12 + 12 = 24 (toAt E). Bidnosidb: 12 roa H i 24 roaHHr.

rpr.tcr., L.

41 96=O,orxe, e neprJa

6pHr eaa-

IlaroBllrrs 6acenn (1 - norc o6'€M) i nep a rpy6a Mor{e Ha.t ronrH, npallloloqlI cauocriitro, a apyra s (:. + 24\ toELr'J

197. Hexan trorpi6Ho noBHrrrr-r

ioro

3a 1 roAttHy neprra IlanoBHroe 192. y = kx

b, k + O. O6,racrs

Blrpasrrsqepe3

e[rnaqeHin

v,roh'=v b,,=+,

-4. OcKin6RU

oaHo3BaqHo

ra rpy6a '" ,rafloBxro€

"=it-i

leni',nHa3a Hicrb, sa yMoBoro fr + 0. TaKrM qrrHoM, o6epseHa d}].'HKqis a,= ia ; Nn qii v = kr + b reri € niEifiHoro. 193.3a

l(r) qI-Ix

yMoBoro y =

HenapEA

Oyllnqis. Hexarl Ol.llltqis y,(r) o6epHena

BnpaBx Arn noBTopeHHq

[4 > 0) - ycs po6ora, sriy rp€6a BrrcoEarr. flepnllIii po6irE{x

roaagy BiH

BiAnMiAb: 3a 1.2 ror]j]l r.

276 llliAIrEEPA Mep3ncK A. f. ra

aovra

_ x24

3a 8 roam po6orn Apy-

1 fo,qrrEy, npaqrolo.ru pa3oM, rpy6r HatroBrrolorl'

I ^^(r 20 lrtrrZq). )

ro.ar-rH

apvloi rp\6 B,rxoHaHo

t :

po6orH. Ma.Mo pisHfl'rHs:

s__2tt.t /1- r ) 2 __f 14 _I 10 r : r-24 \: t,24) 3 r-24 ir 3 42. + 9Ot + 72O= t'+ 24r, t+O, x+ -24| x'- 48 x 4,=24r.17296 r,, = 24 t 36; ' = 60 a6o it = -12.

72O=O;

Brrco-

YMoBy sanoBoJtEEs€ qlIcno 60.

po6ir-

3a 60 roarn MoJ{e HatroBHtrlr 6aceiis nepua rpy6a, a Apyra

Aplr{n 2V ""..""" +. nrrc BnrcoEye Bcro po6oay Bs 30 roAn$, ro6ro sa 1 roAr.rHy BiH BrRoEy€ jl. Pasou AA50A5A--'"30 1 . v.rc pobory pa3oM BoHH Bu3a I roAr.rsy BoHr.r Br.r(oHyror6 20 30 60 6 A:65A_6,46 roAxH. lobro - =;=l.z r-oAxBu. Eye Bcro po6ory sa 20 roarn, ro6ro sa

roai

Tarir-rM.rrIIoM, 3a 8 roalrs po6orr.r apyroi rpy6r{ ii 20 roallH cyMicroi po6orll repllloi

Ao Aa-

Hoi. fpaoil{r.r OylIxqifr cr.rMerpr.rsi BiAHocEo 6icellrpncs I i III &oopaslrarsr:( RyriB. IpaOiK Aanoi Ot'EI{qii cnMerpr.rHri BiAHocEo ro'rRn O (0; 0), roMy ii rpa$iK O]'EKr{ii yr(r) re'rc cr.rMerpr.r.rErii BiasocEo qiei rocKs, ro6ro y,(-r) = -yr(r). OrrRe, yr(x) c EenapEolo SynKai.rc.

'194. Hexan.4

I I ,t ,tro.

j^,.

x+24 ".

i,1l

BiAnoqiAb:

60 rcllrl{

sa 60

+ 24 =

84 roAnEr.

5. PiBHoclrnbHi piBHgHHq. PiaHeHHg-HacriAoK. PiBHoclrnbHi HepiBHocri 194. 1) Ta&, 60 Ha MHor*{rlri

(-€; +-)

t{rcno 8 e xopeue*r

i repEoro, i

Apyroro piB

2) TaK. iH. AKaaeMiqHr4i piBeHb

i:iiii:.ffi;fliii:jiuresPA Mep3ncK A. r. ra

iH, aKaAeMiqHnn pieeF.s

l;l:l

zzz

Hi,60

Ha Msor{nHi

(-*; +*) repue piBEtHHs

Ma€ oArH

liopillb, s&ai AopiBnm€

5, a apyr. piBseHHr - ABa xope$i: 0 j 5, roMy RopeHi npyroi'o pisnnFBq nF. peEsM! rep oro.

Ro-

4) TaIt. 5) Ta&, 60 aHi lep e, aEi apyre piBEnEHn Ee Maror6 riopeHiB. 6) Tan, 60 trolcrre s piBnsHb Ma€ 6e3niq nopesiB fi o6tABa piBEsHEs 6yAr,-nfti BEa.reliss t. 7) Hi, 60 &opeHeM rep orc piBEsIrEs Ha MEorrinEi ( *j +-) e qucno 1, a Apyre EqEEn Mac

pra KopeHi: I

i l.

10) Tax. 11) Tax. 12) TaR, 60 na Mso}I{I,IHi ( *; 1) \-r (1; nopiEb .r - l. roMy BoHU pisHocMi6lri. 13) TaR.

Hi,

2O2.1r Ia'/".2) Hi; 3) Ei; 4) tri; 5) raE; 6) Iri; 7) lri, 60 ftopeEeM piBHnHEs 2r + 1 = 5 e.ircno 2. ,firiqo o6taABi rracrsEi riboro piBHFIlEn troMEornr.rr IIa (r + l), ro oAep*cr Mo: (2r + 1Xr + 1)= 5(a + 1'), 2r' + tu + 1 = 5x + 5, 2x' 2x - 4 = 0, r' x 2 = 0, 'to6ro t = 2 a6o )e = 1. Or)rce, &OpeEi apyroro piBHnHHn ne € xopeHsMn nepnoro.

1)r+

3 > 6;

+-); 4r<

(3;

12i x > 3,

r€

(3; +-).

Ili

sepiBEocri

€ piBEocrnbEzMrr. 2) (x + 2)'z(r+ 1) < O

+-)

trepDe

ir+ 1< 0 ae e pianocr-r.rlEurrur-r, 60 MEoxcnEom posB's36iB nep oi irepilsocri € r € ( *; 2) u (-2; -1), a Apyroi xe( *; 1). - a posB'ssnoM sepiBHocri 3) (r + 2)?(jr + 1) < o, poBB'ssKoM € MEo,r{r{Ea ( -; 11, r I ' 0 ( MpostsHa ( *: -11. Orxe. qi RepiBHo.ri 6 piBHocr{nLts vs.

ii apyre pi

1.1, 1 a.0 e MEo!@ira(--;O)u(li +-). P$B's3rcoM HepiBEocri r > 1 € MHolcrHa (1; +-). MHorrorEu IIe cniBfla,qaorB, roMy qi lIepiB4) Po3B'sBKoM HepiBEo"ti

199. 1) TaI{, 60 KopeHeM xoEclroro s l{t{x € qrcno 4. 2)

Har'z+1+0(reopeMa).

203,

8) TaK. 9) Hi.

x=1.

+ lr(r' + 1\ = 3(" + 1) t 2t + 1 = 3 piBEocr.'nbsi, 60 apyrc MoxHa oAepr{arr.r s nepllloro, sRnlo o6BABi q6crrs6 nepuroro piBErHEfl noAinnrr

4) PiBIrsnHs (2r

60 Depne piBHsHEs Ma€ aBa rcop€Ei: 0

1, a Apyre piBHsEEn oAxn HopiEb

Hocri He e piBHocrnbExMr. 5) Po3B'.a3rcoM HepiBHocri,

x'> x, x2 r>0,i.(a 1)>0€Msonrl-rlla(--;0lu[1;+-); [1; +*). MHoninlrn He ctriBtra,qarorr,, roMy

posB'.sBKoM EepiBEocri > 1 € MHo{r Ha qi HepiBHocri Ee € piBrrocrri6srMr.

3) TaI..

4, TaK,60 r{oAlte r piBHeHb ne Ma. HopeHiB.

6)(r+4)'<0, re 6:lz

5) Hi.

6) TaIi.

2l< 0, r€ Z. HepiBsocri

€ piBEocrnbHr.rMrr.

(x 3t'(r + 4) < 0t r + 4 < 0 t x 3 = 0j r < -4 i = 3. MEo,IlnEoro posB's3rdB e MIIoJxrHa ( -j 41 u {3}. PosB'ns$oM EepiBnocri.r ' + 4 <0, r<-4€ MnorrcrHa ( -; 41. HepiBEocri He € piBsoc*rnr,EnMlr. 2) @ 9l'(x + 4) < 0; r < -4. MHo}I{rHa (--; 4) e po3B'ssnoM qiei EepiBHocri. ,4r.8 EepiBFocti t + 4 < 0 po3B's3KoM e MHoxcnHa (--; 4). Or)$e, qi sepiBnocri

2O4.1,

?) TaK. 8) Tal{. 9) TaK.

3 4, x ts R. -r 3.5. fioMy piBHocn,"6He pisHsHHs -r 3.5 = 0: r. R, r r-1. iovy piBHo.xnbse piBHa\He r I 0: 8 xopeHiBEeMa,. ioMy piBso.xnbHe 3),r+6=,r-2,re R.0 I Esr:+1=0; ql L I O, r F { -; l).r (l; r€), KopeniB Fe va€. rl

2OO.7) 2x 2) lxl = 1,

iolay pinnoca,r*re piBHnHB'

;

{--? ' g. pooB fl3tsoM c r'r'o)nrHa (-*; 2l (4: --). x4 --. Ans nepiBHocri, 2> O, r > 2 posB's3KoM (2: -). Ui HepiBHocri Hc c piBHo31

41 1E <

0, posr'saxoM

e .rxcno

-\,.--

-Y--

0. ra < 0, poBB's3KoM € qrcno 0. IIi HepiBsocri

piBHocrrnLHi.

205" 1) PiBEsHEs x'= r peEeM piBHsHs.fi

Apyre piBlrnHHs 4r - t = 8 + 3 MoJr.I{a oA€p{arl{ 3 nepllloro 4t 8 = t + nl(rrlo Eepen€crrr AoAaHRr s oAniei cacrEEE piBHsHns B iHtrry .racrr.Hy 3 nc)rHrvr 3Ha,{aMl,l. ToMy piBErHur pjBnocHn6Hi 3a reoppMoro. 2) PiBHssEE piBsocrnbni Ha MHor{nHi (-*; +-), 60 (opesi repllloro piBEnHHn 2 i -2) € KopeEsMn apyroro piBri.flEn.n, i EaBnaKrr: &opeEi apyroro piBlI.sHH.s (2 i -

-I-I czoci6.

e KopeEnMtr nepuroro piBE.sEHs IIa

3'r-5 'r I 26 HrrrHr Lr ls

{treourc

rii

caMiri

MEor.c1-IIIi.

DiBHnHHrr:9r Ib jr 6i gr '21, r=11 .10r..

,r = 6 re]:{ Mac qi piEEsEEs piBllocrn6Ei.

KopiHb r.

18 Orx.. ;.

(A60 Apyre piBE4sEs Mostsa oAept{arlr, sKrr{o o6tABi Ha

278

Ha MHosHHi

qacrtEr nep oro

I -r

e EacniAKoM

r'= r,

a"re se

piBr.sIIIIs r = 1, 60 lropirlE 116010 piBEsHEs e Ko,v'z= x € kopeHeM piBEsHHs

xoxes xopinr piBHeEHr

2) PiBnsEEs

0 r= 0 e EacniaKoM piu"""""

3) PiBFnEHn

I'9=

{=f.

€ HacniAnoM piBHsHHs x3

= 1.

4) PiBEnEEn ,r = 1 e EacniAKoM piBnssrs.r3 = 1. 5) PisunrlHs

r'?= 36 € nac,rirxou pinsgssg

6) PiBrr.sgrr.a

t'=

{1=

r-6

.'--!= = l-J=. t+2 x+2 pin""""" t'=-0.

4 e qacniarcoM piBHngns

PiBHslrHs:t'- 1=0

e saciri,qxoM

6. 3a reopeMoo 4i piBll.sHss piBnocrnbHi.)

i::IiAIrEEPA Mep3rrKA. r. ra

iH. AKaaeMi,{H]4t piBeHL

lri:l:iiiilti{lti: AITEEPA Mep3reK A. r. ra

iH- AxaAeMiqHan piBeHb

tii:

229

206. 1) PisssEgs.!'=.r s sacrirxotr{ pisHalrlr.E 2) PiBssHHs

r(r -

1) € sacriAkoM pilHsHss.,.'?

a) piBH'HHe ,r, = 64 c Hacni!{ord

pt""'"'"

= 1.

+ 1 = 1.

_i.8 =;],

r^- J ^ s, 1-. ,+3 a+3 207. 1) PiBHsHs.s 3r - 5 = 1 piBEoc',rElre piBHssEIo t = 2. 2) PiBssHss (:r - 3)(t + 2) = 0 piBEocrnEEe pisHgHsrc i:'- rc 6 = 0. 3) PiBnsrIIIs 0 . r = 0 i 3r - 5 = 3t 5 piBlIoclrnblli. 4rPiBHqhHr0 jr- I i 0 .r=3 - piBHocr,rbsi. /lii:l:.:{.!:.i:,!! 208. 1) (' + 3)fl') = 2ltl + 6, (jr + 3)(flJ.) - 2) = 0. IIe pi:gssgg naae KopeEi '=13 i Rop€Ei piBEsEns f(t) 2. ToMy, sftqo qe pitlrssHJ' 3aMin'rr FIa piBHsEEn l(.t) = 4) PiBHeHHn

it:l:i'i-:a.a:.i::::i::

r:=9c

Hac,linffoM piBHflBHn

= Mriox{{Ha xopeHiB BBysurLcs.

zt,gn.qo pluoono"

213.1tx,+t-6=0, lx, +.r, = -1. fr= a. x,+x-6-(r+3)(x-2); 'x,= 6: Lx=2i 2135-2x-r'=0; 2r-35=0; + x1= -2. = )r, lx x,+2x-35= ( t2-2x+ 35)= (r+?Xr-5);

I(') t'+1

raMiHr.,ru Ha piBusHss

f(.r.)

'x,

3t2x'z t

-35:

r. =

gx 18 0:D=81 -4 2 ( 18) 81 | 154=225t,r, = -9-15 '4

,"= j#=+= 6; zx, + er . = 2(x + o) = rzr-axr+o); |)r:u 4) r' 16x+3=OiD=16' 4.5 3 = 256 - 60 = 116; ,, = 19# = 18

,, = tu;tn

sx"

- rc,

+z =

s(t |)r,,r

'f,

= ru" - rx" - rr.

u. ro MHor{,rna

6. MeroA iHTepBaniB = r. + 1, n&e Mo)KEa sarrcarta rall: (.]r + l)(f(r) 1) = 0, rrMe 6irBrrle nopeEiB, Hi,{ piBEsHEs t(r) = 1 (qe r = -1 i (opeHi piBEn'isn flr) = 1)' ToMy MHor$rrHa xopeHiB sBy3rrr.cs. 3) PiBETIIHS

(r + 1)l(r)

f(4. c(x!. q'i+1 r+1

Uc piBHauH' Ma€ kopeHi. nxuro x F -1. PiBh'HHt 6i,rblll xopeHiB. Hi]l. raHe. 1o\ry MHo)}{HHa nopeHiB po3llrtrpltrLcs.

209. 1) HepiBHicrb 2) HepiBHicrL 3) HepiBgicrb

/lx)

= s{.rr

foryeMoca Ao BnsqgHHg HoBoiTeMx

(5i -t:

o; lll >0. ie ( -i s)L,r-5:--r: .r+5 t r.'5 2{r r5l - x-5-2r-10 tt>-'-<u.<u. 'xtb 2 2tx+5) zlx -51 r €( -; 5) ! (-5; +-); 8t +>O. jr€ ( -r O)u(0: +-l; sr

*:0. x'+ l

-71 u

[-5

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1) Ocxi"nrxu .r e (2; +-), ro sEa.{elltls Bvpa}y , - 2 € AoaarrilrM; 2) oclcirbrir r € (-3; -2), ro sHa.reH1is Btrpasy x _ 2 € BiA'€ME!iM; 3) ocEinbrir r e (--; -A), ro 3lra.reEns Brpasy x - 2 € Bi,q'€MIrnM; 4) oc&irErcr r e (5; 9), ro ssa.resHs BrIpa3y .t - 2 € AoAarH{M.

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(5; +*);

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r > 5 e HacniAEoM IlepiBlrocri, > 5. r' < 0 e IracniAKoM EepiBnocri r < 0.

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< -4 € EacniaKoM rrepiBEocri x < 1.

211,1)(r-5)'z>0,r€( -; 5) u 2) (t - 5)'> 0, , € ( -; +-); 3r(x.-5t'<O,)c€A:

214.1) (i + 1Xr - 2Xr + 5) > 0; r € ( 5; 1) \-/ (2j +*);

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lx I 3. fr a. 2,r.-2xjr o.b, v^ lr r 4t ! l: rir 4r{x lr r € ( -; l) u lo,5;21 u (4j +*);

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1.,1):

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r € ( *; -8) u [-1

+\' -\..-"-\,,- \ 1i€ 53032)c 54

e) L, (11; 2,4

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l-V-)/T-y-Y-,6346

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4l 1x'z+2x-1 -

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DpHiMaFroAarHi

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-1t--=- a'---!

kr.rr rapa6onE HanpaMnelri Bropy, roMy Blrpag r' - 4, + 5 llplti.tM e AoAarHi sEa.reHHfi.

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284

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t 2, < o, rx 3f{r 1)tr 21 10, rE[ 2; 1]ui3]; 7)(:c-')'(t')+x 2)>o, (r.-3)'(r-1)(r+2)>0, r € ( -; 2,) u (1; 3) r-, (3; +-); 8)(,r-3)'z(r'2+'-2)>0, (r-g)?(r-1Xr+2)>0, r e (--; 2l u [1; +-). 223. 1) (r 1Xr + 3)'z(r 2) < 0, jr €

pa6onu EarpsM,'reHi Bropy, roMy piBsa1lH-t Ee Mae

l(opeHis. MBoroqneH.r'z-r t € R.

{4};

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fx,+',-a. lx =1. 1,, *, =a, l'=a, (2!+1),(t-1Xr-g)>0, , € (-*; -0,5) u (-0,5; 1) u (3; +-); q Qx + t)'b 1)Qe 2) > o, r e ( -; -0,51 !, [ 0,5; 1] u [2; +*), ro6ror€(-;1l!J[2;+d); 5) (r - 5X, + 4)(r.'+ 6r + 9) > 0, (r 5)(iu + 4X, + 3)'> 0, , € ( -; 4l u [5; +-) u {-3}. 224- 1\ t'(t + lxr - 4) > 0,

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'',t l- 2l , o. {' t,ral(1i.1 ' x'-6-r+9 3)' re( -; 5)!,(4; +-); t'+t-20 >0. lr-41(r+51 zl' -. (x-3)' .r'-6.r+9

zzs. t1

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285

lx l') lr lr x 2-t I , '2, 8 (r 2r(i | 4r' r'' 2nr I ll a E (--; 4) u (2i +-)i lx-ll': 2"+1-n-0, n, - I.r' + 2:r 8 (x 2)(r. + a) re(-;4)u(2;-r*)',11); t" lt r-,2.x+1<0. -r _0. '' r'|+21 8 (jr-2Xx+4) ,x€(.1;1),J(1;2)j br

R, r.

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a; 2).

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1-I.

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t€r

A]nfEEPA Mep3neK A. f. ra iH. AKaAeMi'rHral pieenu

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286

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u (0; 0,5) u (1; +-).

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229. 1) (3 r)3(r + 2)r{x jr € (1; 2,5) Lr (3; +-);

(t+2\/'-3\ <0, 4,5-23' r € ( 4,5; 2) '.r (3; +-)i ,_ I Z, lr-l|n! ll ,1..1ll 2irlir l) o. 0,,_l x(' l) xl r." 2x+1 '"'-r' 2r'!+2x <o, ,41: jrl!<0, 1"trJl;\.o, :,l](x 1) 2a" + x-7 >o. 2x!'t r 1=o,r=1 +8=9,

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(-*; O) u (1; +-); -r,r-ri3 o ^ x-3 o' I -, 1 2x-r r;; ;,

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227.

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287

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/.=\ /.=\ /_;\,,---\ dIIa-

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e (0; 1l u [1; 2] u {3} = (o; 2l u {3}.

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+-) u

1:-:;!i+zyr-n>0,

4, (, -3r^114+5, - <0, srcqof,-3<0,r<J [ 2t 71, '"ro6ro r < t-2t 3] u {'Il. Bidno4iAb: r e t 2;31 u{7}. st @" - zlJta - ,' <o, t.' - sttx + srfa - x1a -'1 . o.u/i+ *rre xt

)'7-7v'--. 2-/A7'

-----a21)

--\,..+t\,--_+

--------------

-4 ----1i':"":--:--\

----

BiAnosiAb:te(4;4).

BiAno6idb: E.piBl{lcrh He Ma. porB arKrs.

itjl! ArrEEpA Mep3rrK A. r. ra iH. AKaaeMieHrt piBexr

€ t1; 2] u {5};

Ea MEo,{rI{i

+---\----

z8s

zE (3;7r. - ""

3rJt4 + 5,

BiAnosiAb:

yKarlrMeMo Es MEoxIrHi ( -; 2) u (2; +-), Ae 3II"*"""o \f,L A roAi snari AaHoi HepiBHocri Bane)&arlrMe BiA BsaRa Blrpasy (t- f)(r + 1). UIo6 6yrTa BqRoHaEa yMoBa, rorpi6Ho po3B'fisarx ---IIepiBHicrE (, 1)(r + 1) < 0, x e (-1j 1). 3Ha;AeEa (--; (2; +-l MHo'lrrria IIe rlan${Ifr6 MI{or{I[d -2) u rovy aala scpiBHicrb Hc Mac porB'rrtsiB.

0,,

t' - 5x 14= O, 5+9 7. ,t 5-9-- -2. Ha usoNntti (-2i 7) uryxaruMeMo po3B fl3xn I z EepiBHocri. 3a yMoBoro MaeMo: jr 3 > 0, r > 3.

BiAnoqiAb:

po3B'ssxr

to<

s){4 + 5r - > 0, ''z

Ha MEoxcnEi

rxr + r)uG zX,+a<o. ic}rrr.nrcuox' a-0. ,--\/'-=-\/u [2; +-), ane aana l{et---

lt+

- 5r + 4) >

,=25+56=81,

srpary rr:4 r e (-*; -21

+ +r.[x"

jr e (3; ?). -x2 + 5x + 14 = O,

-\JV - +. o, (*

ro6ro Ans

-rx

235, 1) (, -

< {).

2a-3 1 2t2xt3t rx'/,x -t2l x+12 2i"t'+x-12 (r+4)(r-3) <0, 2 !'+x 12 r:+3:r+18 - -{,!"-Jr-18)<u.--T\,,--\,4\,/- \,r-(.r + 4X.r - 3) tr + 4)(jr 3) -4-336t r - ( -i 4) ( 3i B) ,(6: --). 1"-6lI+,0. (.r 4)("r

(tc"

e\ @" Sr++\Jr' -Zx+tO ) 0, .r e (

MnoroqneE r' - 2, + 6 npd;Mae AoAarni sHa.relrss, roMy sHa& Aalroro Apo6y sa"'re: ){rrrr, BiA sHaKa sllareEExfta, , € ( -; 0) \-] (1; 6);

aoaarnri, ssrqo

AaHa HepiBHicr6 BsrcoHy€rr.cs Ha rlii MEorr(sEi Ba yMoBn (r2 (r 1X, - 4) > 0, snrqo r e (--; 1) u (4; +-). 3HafiAeMo treperrH MrrorlnE: ir e (-*; 1) u (5 +-). BiAnogiAb: t e (--; 1) u (5; +-).

\,,?\,,-T.\?'=-\/--

u (4; +-); 2)'t'Y 3}i <

€ (-1; 0) u (0;

------i-i ---

r€(-; 2)u(5j+-).

t _t 2, . (5: _-)u{11: 3t !'lt' ll . o. 'r'?lJ' - I,(r' - U , 0. r 4 x-4

--+-\-,--=\-zT

-). royy AaHa HepiEEicrb BnKoHy€rbcs. rRrlo (-r? 5r. 4, 0 Ha MEoxfisi M. Orrfte. lx 4X.r I ) 0i r. e (1i 4r. SHafiaeMo nepernH MHoxrrs M i M\ (lt 4). -v e (1: 2). BiAnosiAb: t€ (1;2). t7 1"" - t, + t1..,Q 7a11s,s. SEan Brpasy Jl-?r.10

ililf::;i"t+li ,iilii-::.!1:ri!t

sliqo r € ( -; -2) u (2; +-)

3Eari Aanoi HepiBHocri sen€nirrr, BiA sEaxa Brrpasy .r2 - 1, rorry r, - 1 > -0, (x lxju + 1) > 0, sRqo r € (--; -1) u (1; +-). I]eperEEoM aBox MHo]r{Ilrr € Mrro-

iii:ilillttilii: l0

Yci rnP,

AnTEEPA Mep3rsK A. r. ra iH. AxaaeMiqHrn piBeHb

lou.,r.l

i{t

2a9

(r'

zs).,/io

--+-\

.,/io '"pu" '0,lqo6 '" 'o 4:''4). 46Ha HepiBHicrb

BUsi ( xoqysria.F. troBfiHHa BHKoH) sartrc't HFpiBuiclb (x 5\(r + 5) > 0, ,. € ( *; 5) \., (5; +-) BEa;-

Ha MHo)n

AFMo

nepprlrH

A. AaHa sepiBHicrb

BnpaBl,l

_-.',-'+. 5\- ---zs x

Ar9 noaropeHHt

.-\,5-445x -a--a

Biano8iAb. pos3'ssftiB EeMae.

r\ @" zli|Jta - ," < 0. Aalra EepiBHicrb BnrloHy€r6cs, sKqo 16 ,' rc'Eil4; 41,"G'-25)<O,(x 5)(x. + 5)<0,jrc[ 5; 5]. SHaiiaeMo reperrE MIIonitrE: , E [ 4; 41. .[aHa EepiBnicrb Brriolly€rbcn, srcqo t e [-4; 4]. BionosiAb:tel4t4l. 1'

r:f

::':.:.:.:.1:.::

1r' :r).,/ia-l !5al4i4l.

<0.

+4, 60 +4 € [-4j 4], a

PocB"rsIloM AaHoi EepiBtsocri

na MHo-

3Ha.reHHfl

BiAnosiAb:

x=-1, a=3BiAno1iAb:

236. -L s -L. x'-9 r" I

ln:=o'

Po3B'fir{eMo

24O. 1)

," gt t" -g' -{ .o-

]*' e-''-e'uooz.

l=:."' t

€

(

3; 0l \.r (3;

\e, +zs

-6-3r

+-);

:-\-/-+-\7--r-\-/--

l=:'o'

ti---t- 1

lzx

"s '

,, ]'' "'-n=u ]t n'u,_r. o: i-5. -j-. o, tr.'-g |,r'-s (3; +-).

t3.01 u

lI-1 -o.

[ll.o.

j1",',' x - r,,-, "-.1+1.,:-:u' l',,-iu 1,, *^ rs, 1,, ro. ,. lo.

BiAno6i0b: 2 napv.

Po3B's)+rFMo rr.{r'reMv

r,f, ]*"u llr

o' ; 'o I r-1 -- I6 -0,

excMo.r.reMv r2r' ]''

'"^ 1'o: r? 16

BiAnosiAb: crrcre!\a Ee Mae

241-

u=1

lr',snqor'-t.

x - ( 4i Il' (4: --).

(r; U) | G,: v).

I -r-1 .o,

P..'R

= 2.

c creMy:

[.' -,' .0. 19".0. r, l.r'-e .r' e lx'-e

Bi1nMiAb:

lv ,' =,, 10-2x I2x+5s=ro: !t= 5

BiAnMiAb: qy'lr{\nr 3pocrae Ea npoMir{Liax ( -; 1l u [0; +*); Oyslrqis cnaAae na npo Mir*xy ( 1; 01.

,..

Bilnosilb: (4;11 u (4; +-).

290

ai{: ATTEEPA

Mep3neKA. r. ra iH. AKaaeMi'aHxi piBexr

{iii:lliil:iiilti

:il::iJtiilitiai ATTEEPA Mep3reK A. r. ra l0*

iH.

AKaaeMi,{Hui piBeHb

i::]i

291

s3. cTEnEHEBA OvHKqlC

256. r\ a = f iy.=zxa; x6 = 2a4, a1(z' y = 8; (o; o); f"E; s); (.8; s).

1. CTeneHeBa OyHxqit 3 HayypanbHirM noKasHt(oM 242. v = i6. Toql(a B(2; 32) Eate'Iirrb rpaoiRv OvErcqii v = t5; roclca D Irane){r{rE rpaoiEy oyEnqii y = ,i.

(

3; -243)

/ r r)

243, rpaoiK QyFrqii y = .r' rpoxoau rb sepe3 roqKn: A(2: I 6)r Cl -

_12 -12)t t2=a 2t. a , i;.r=

244.A12i

ncn a - -

B(-8i

3):

nor a '

rpa+iK Svsxrii

-3

-fi

245. C(3:

18):

fipri

-8

t.J.

a = o,

ra i A = -27xi xa = 27x, t(x3 + 27)=0, = -3: a = 81i (0; 0); (-3; 81).

257. y = x6 i y =

a,=

2\-o,x-o,,=-"E,

a"= 1,

,="E;

t(x+ 3)(r' 3,

f , ri = ts, x3(z' - t) = 0: r3(,r - lr(r ys = 1; (0; 0); (1; 1); ( 1; 1).

+ l) =0.

=o,a

+ 9) -

r =0. r

0,,

= 0,

l. r = -1:

2\a=@+

258.1)a=x3-1i

v = axa opoxoanrb sepe3 roqKv,{.

'" = a (-3)', a = (-3) '-st'= -.

a' 27

rpa$ix (DyHHaii Dpoxo4 r!, 'repe3 roqRv B. 18 =

33;

_1a 3- 3.

rpaoilt SyH$qii y = ai3 trpoxoAxrh qep€ roqnv C.

3) a =

4)v=ra

-t";

DF2;64\:64-a (-2)", a _-=-8. tlpu a = -8 rpaoiK O],slcEii y =

npoxoar'rrr, 'Iepe3 roq}tv D.

246, f(xt = x's, 1) f(1,4) <

l(1,s); 2) f( 7,6, > l(-8,5):3) l(-6,9) < l(6,9); 4, f(o'z)'> f(-12\'

247-ftx)=x. 1)

l(20) > l(1?); 2) feaa, < f(1,5\',3t f(-52\ <

24a.

x'zo.

1) ^x, t(s,6) < l(4,2); 2)

249. l(x) = r{. 1) l(9,2) > l(8,5); 2\

iso.

1) '" n

45',.

l(-6,7) > t(-5,8); 3t f(-2,4, = f(2,4\t 4\ f(-15) > ^2\.

f(-t,I, < 1( 1,2\i

3) (1e) = l(-1e); 4\ f(-7) < f(s).

= 1600.

2) n -

5)y=(x-1)ai

trapEe LarypaiEEe qlncnoi aBa riopess; EerapHe sarypanr'Ee cltcno: oanB KopiEl,.

.82 2\ t' . -;7, x = -il r = 5i 4, ,.a=-16: xe O. 3) =81; t=13; 'i 252, 1) tx = -27 , r = -3; 2) t' = 0,00032' x - O,2; 3) xo = 64, t = !2t 4\ 13 = -l' reA. 253.1) 16 = 2, rarci 2) .'5 = -3, rali; 3) t? = I, Ei; 4) t6 = -10' IIi. 251.1)

1'' er,= "2

= 32.

,s4.[ ;J', i-?]',

t ll', (-fJ'

255. (-0,48){i (1,06)'i e2,12)a',

(

3,25t4.

292 iili anrEEPA Mep3reK A. r. ra iH. AKaaeMi,{Hur

piaeau i:3i1*ili:iJlit

iiiiitlillllili

AITEEPA Mep3rrl( A. r. ra iH. AKaAeMi,{Hr4t piBeHb

:iiii

293

259.1\a=t3+3i

26s. Iv = '"'

2\y-(x-3)3i 3)a=rn+2i

l2x-s-3=o;

4)a=G+1)\: t" 5\ Y= x',

6\a=

a=2x-3; ,{oanoro KopeEF.

xn'

/(r) =

I:r'.sxuor<0.

IlJr.rxqor>0.

r ' -r' ,, r,,, {r"r axuo 2. x: I '*nro

lit! ::4.'ii:.ii:: 260, 1) l(.!) = r's, js e [0; 2]. Ha rrBoMy npoMi,r.fty {DyErirris spocra€, roMv EafiMesIIIe slla.rellHn Bolra np[IiMae, nriu{o, = 0, ro6ro 03 = 0, a Hafi6in]'ue - qtrqo t = 2' ' tit;ria!!i:.! ro6ro 23 = 2a 2a = 16 . 16 = 256. 2) t e f 2i 11. Ha qboMy npoMix(y OyHxIriE cna.4ae, roMy san6irLrre sHa.reHIIn Bosa nplriiMae, sKrqo t = 2, ro6ro (-2)3 = 256, a nailMeErre 3HaqeElis nKulo r = 1, ro6ro 13 = 1. 3) e [-1; 1]. .fl{rqo jl: = 0, ro OyEtcr{in rpl,liMa€ HaiMeEde sHaqeHss' 03 = 0'

' sknroJ' = 11, ro &ys!{qis rpriiMa€ Haii6irLre sHaqeIIHs, ro6ro ( 1f = 1a = l' 60 sa rpoMixcxy [-1j 0] Bosa cnaAae, a Ea rpoMi]cRy [0; 1l - 3pocrae. 4) (-*; 2l. Ha qboMy rpoMirri(y &yllrlllis craAae, sail6ijIblne rr rre MornHa, a HaiiMeHlrre 3HarreEEs oyllRqif rprfiMae, sntqo x ='2' ao6'to r

2)3

3HaqeHnn

3; 31. Ha qboMy npoMi}}{ny OyExuiF 3pocra€, roMy Ea;6inblne 35 = 243, a HaiiMeErre 3t{a'{eHEn nlcqo

rpriMae, sxrqo t = 3, ro6ro

3, ro6ro ( 3)i = 243. 2; 0]. Ha qboMy rlpoMiJrtl(y OynRrlis 3pocra€, roMy Hafi6inbl$e 3Eaqet{Hs tbvHKris np iiMae, nriqo t = 0, ro6ro 05= 0, a EaIiMeIr e 3HaqeEEn $11\o r'-2, 10610 ( 2)'. -32. 3) [1; t--). @ytsl(llis Bpocra€, EaiiMeEsie sHaqeEHn trpriiMa€, sR[Io r = 1, ro6ro 1r = 1. a Hai6inB]le 3Ea.IeHEn BKa3arrr He Mor(Ea.

r= 2) [

262.1\ t3= r + 1- aBa

Ilopesi;

Ha npo}tiniKy (--; -1) OyH Iis spocra€, a Ira rpoMi){Ky [-1; +€) cna,qae.

[x'.sxuox.o.

265- tQ)= \ _ ./r. nxxro ir > U.

256.

261,1)f(rr=t5,re t

Ha IlpoMirftI(y ( -; 0) OyHKrriE craaa€, a Ha rlpoM { cy [0; +-) Bpocra€.

2)x5=3-2x lcopiHb;

oarrE 3)/=0,5r. Irorc $opeEn.

]Koa-

na ,'poori*rry (--i 0) OyE(qis spocrae, a Ha npoMi*rEy [0; +*) cnanae.

266'.1\ xt' = a

qiei OynKlrii cnMerpltqErn BianocHo oci Oy, y > 0. y = r" - lpaoilr a = a - 6 - rpaoiRoM qiei OyEliqii e rp€Ma, Ena npoxoavrb 'repe3 ro'rKv (0; 6). flRrqo (, - 6 > 0, ro6ro a > 6, ro pisH.nHH.n Mae aBa lropesi; sr{qo d - 6 = 0, ro6ro a = 6, ro piBEsHEn Ma€ oAIrIr RopiEb; .slirqo d - 6 < 0, ro6ro lr < 6, ro piBEsEHs Ee Mae KopeHiB.

BiAnoqiAb: 1) a > 6, aBa l(oped; 2) d = 6, oar'tH nopiE6; 3) a < 6, xtoaHoro rcopeHn.

2)'^=a,+7a-8(1), *4 ryaOiK qiei Oylllcqii crMerpt'rErn BiaEocHo ocl O!, ! > O. tbrrJ\oa'+7a 8=0, roa= 8, d= 1, roAi piBEsHrIn (1)Ms€ oAtlr EopiEI';.sHrqo a2 +7a I > 0, ro6rod€ ( *; 8)u(1; +-), ro piBHnsHs (f) Ma€ aBa lloperii; sllqoo'+ 7 8 <0,ro6rod€ ( 8; 1), ro piBEsIrEn (1) He Ma€ EopeEiB. Bionosi.Ab: tt:1"n\o (r € (-8i 1), ro piB1rnlrHs IIe Ma€ KopeHiB; nKqo a € { 8; 1}, ro piBEnHHE Ma€ oAlr]i RopiHb; nErqo o € ( -; 8) u (1; +-), ro piB}].'sH.t Mae ABa a=

lcopeEi. - ts = 9a a3 (l). rpaoni Oysr{qii y -

267

caMerb@sr; gi{lloc:do oci Oa, a > O.

'3 a'z)=0,4(3 aX9+a)=0, a=0, a= 3ia=3,1o fiKqosa a3=0,ro6roa(9 piBE.'riIIr (1) Mae oar.rE llopitlB.

294

l::i AITEEPA Mep3reK A. r. ra

iH. AKaAeMi,{Hrar pieeHu

illlii-:::::il:!ii:l

i;;iiJiltiil!!! AnreSPA Mep3rqK A. r. ra iH. AKaaeMi,{Br'ti

piBeBb

::i::: 295

gKqo 9a -

03 > 0, ro 4(3 - a)(3 + a) > 0, ro6ro a e (--; -3) u (0i 3), roai piBEsEIls (1) Mae ABa KopeEi. fiRrqo 9a - a3 < 0, ro a e (-3; 0) u (3; +-), roai piBHsHns (1) Ee Ma€ I{opeHiB. Bianosiqb: ttKLr\o a e (-3; 0) u (3; +*), ro piBHrHEr Ee Ma€ xoAHoro nopess; Elcqo ae (--; -3) u (0; 3), ro piBEsEEs Mae aBa riopeEi; sRqo a = -3, a=0, a=3,ro piBEsIIlIs Ma€ oAnH (opiH6.

"@'i)

264. f@J = x^. 1\ tC4') > f(-21, r, rapHrrfi noKa3rrnK; 2) f(-4) < f(2), /, - HenapErdi noKa3slrr{; -

273. r)-a(o; 0), 0 5 - 0. Br.rpas IIe Ma€ BMicry, rpaabilr lle rpoxoalrrL qep€3 ro.rRy-4(o; 0); 2) B( 1; 1), (-1)-' = -r. fpaibiK npoxoarrb qepe3 ro'Dcv B( 1; 1);

3\ f(-4) < f(-2\, n senapgr{ia ronasH*rx; -Mo)ne 4\ IAI J(2\,, 6yr,.r i napH M, i HenapEuM, - napHr.rii 5) f(-4j > f(21, n nol{a3Er.rli; 6')

.frtii:il:::Ja-:::i:

f(41> f(-2\, /,

Moxce

6yur dapll

=( ;)' =* rpaoi* se rpoxoa'rrE.repes ro.{xvB; roqfty c; t3 rtl.) (i)" = * = rt rpaabi& npoxoat rE.repes "l.1, . {Jr) -li-l =i. rn.oi* He npoxoruflr sepe3 rocK} D.

:ti;Ar'.'

'u'. 'r

=(])",

' "^=(:)"' z\

1a-01"

zzo.r

=--Jlo-b)'

, *=(;)" s1

a) a- -

n'=l;

/ll

l;,r

rpsoilr trpoxoarrb qep*

c( 1,

-"*y

sr' It 3'tl'-- 243t -

24A-J.

i_rr*i lr.t.:.{1

A(-5; 20), 20 = @ . (

5)-s;

t(r'l-). L24 = ".2'.

", \ 24) 275. y = 6t.

!!.

26=--L.

o=-25691

125

la1 24 R''

l: -3t 8I a=-2q.a:

o I)A(3: -3): -3=a 3{t 3 d 3.r

I r 1. ,,' r(\ -",11. '2) 2= o . r-2\ . , = I2, I\ - I2)l' - 2 , t6 ,

.s.

276. f(rt = x ", flxt = :n,. 1) fl1,6) > flz); 2) f(-5,6) < 2 3

277.f(xr=r". fr 1)

'=1-1=S+,

2t nn-rn

274.y=aat,

1=4-3= 1: ar 4'-13412 12

a'z+d

lli

fpa(bix npoxoArrh qepes roqfty D[-3:

r _ t75+50- 2. :r l2l', rz.sf s, 7,r -a2?. 2 25 50 =?23 50 50 \7) 4.)9 0,1 .9 r0 goi 51 0.5,.4, = l1l-'.1= 4.1= 1. \2J44 / 3rL 1- !. '_ t ' ,.16r, 6r r2.,-s =I \2) =\- z) t2 8 rel) I\2-rl) =l-,11' 271.It

ezJ.

243) \ -s,---L1.,

q (2x-3! a = 1 "' (2x -3!J)'

I 9t? !8367272

ar al

foryeMocs ao BrBgeHHr HoaoiTeM,

H€rapFrM,

:t;lI'lAi-:J..'1.',

liii:ra:t::::i!:i: ry

.r'

"(', *)'

l(18) <

27A. fU) = x

,,i

d.c _ t ll t __.d(c 3)r., d,)r. ,,,_f'I c d)(e d't'd)'z (d c)td'

1) f(1,61>

f( 6,5);

{-e,6) < fls,6);

4) l(0,1) > l(-10).

I =

,*.

32) >

fta,6l < fl-3,6tt

l(16); 2l f|a,z\

f(2,5)t

28).

t ''. flrt = --:.

f(2,21;

3,4) =

l(3,4);

4) l(-18) < l(3).

(t \r'

r') 4l (x -u llx -u"., ) =l-+-1.-

I u)r-c"

1 s2+x' I x!2 xz-a'? x'/

2. CTeneHeBa OyHKqie 3 qi,|rM noKa3H]'KoM 272. a = xa z . I j l' .0"o,* npoxon,'rL qepe3 roqky A; ,'u. [:, ,'u.1. 296 iii: AITEEPA Mep3reK A. r. ra iH. AKaAeMi.rHr,ri piBeHb ii:.:iii::iii:{i:jj e

275. J(xl = x 1o, flx, . xao. 1) t(6,2) < l(5,5); 2) l(-1,6) >

f(-1,7\t

3) f(24\

- f( 2a);

8) < t(6).

x'= 2500; " 2500r r'= r5_. 7l n trapse tsarypanbge {rcno. com} pisssHlrs x' - -l

280.

, -

Eeilspse HarypaibEe .rrcno, roMy

piB

rl{ltil::tl:ij::: AITEEPA Mep3nqKA. r. ra

"""rs

** ,h

ouu Ma€

nop"ti;

oarH Kopixb.

iH. AKaseMi'{Hr,rr piEeHb

iii:

297

ttr' LJ u=x.r'o

2a1.tt!=tx 't'.,

O6nacrB BE3na.reIIHs

{ryHKaii

r(y)

(-*;

u (oj +-).

- zt"t'., =l\tx-zt - !-l ) t 2+0, r.+2,a=(k 2r')',A=G -2r4, D(a) = ( 12)

nicrs:

2) u = ttx

282.1t

ra', 2r

I z. l. z. ,, o.Toai ro x"2

-r'

Hi,

'iiIijfiiiri itirljft:iii

3tx-=-3,

10,

piBHnHHn r.

0. To4i

t -,0.ToAi

j ;

Hi, piBEsstl.s r 2ag,

285.1)g=x'+2. D(. = ( *i 0) u (0; +*).

I i III

2)y=(r 3)'.

D(fi = (. *; 3) u (3; +-).

' tx 3f'

x'= to , r, S

iro .

z,,,

o.Toai x'=-.1

i/-

-'.3i,y

!a ir

qs prBl{rcrb

BI'IKoIlv€rrcs, oo JIlBa

BiA'€Msa.

Bi.q'€MEoro ftopell.fl.

= 2 He Ma€

4)s='3 1.r(1,=( -i0)\,(0:+-),

1" 2

,(/l = ( -;

u (0; +-),

a = x, ryaoinoM

rpncorc

1" 0. x"=32.r'

32r'

r=-i/!.

3 Md. Bin'cvprt kopi'rL.

qacruEa AoAarna, a npaBa 3

l'. l=1.,.o.32 ra 32 t' 32 **-"* fr, 11. I 16'r

ro BHKoHycrb.fl prB

d,yHXqria nepelrHdlor!'.s.

4txs--2.

r**

gxqo rpa,liKx

= 0,3 re Mae BiA'eMHoro IropeHs.

TdK, pisFaHHF

u (2; +-).

d= 2 Ma€ BiAtMErn r{opiHb,

r= 3

0.3.

ii$i#$i

i'l{l ;A:::::::l

piBEEHr'

i u=.1x.

2€.4.a x"

€ trpsMa, sKa € 6ice(' noopalrHarHr'x riyri!. 1

y=-.

y=x3.flnqox+0.ro

Toq&r nepersl]y .paoilliB: (1; 1) i 1 II cnoci6: x= r 3: r==. x+0r

( 1;

1).

T=0,,,,=1,n=11. MaeMo

ro.r(r: (-1; -1) i (1;

2) i/ =,r'?. flr{u{o

rI u=

+ 0, ao u

1 1

3,D(R=(--; 1)u(1; +-),

(.r

6) a =

tt",

D(f) =

( *;0) \,

(0; +-),

1)"

npFva.

rpoxoArr6 qepes roql{y (0; 0).

ro.rKa neperrHy rpaoiKjB:

rpaQrk qr.r qryHKUll

.filga

5)y=(,

1).

cnoci6:

: j

.l1r x. = rr

=0.:r'=s,x=2.

r*'. -*'," 298 iji

/ 2r11 { ].

1) lr, \ tl

AITEEPA Mep3rcK A. r. ra iH. AKaaeMi,{Hlln piBelh

l::itl::liltlil:i

iiiliitiiiiilt!

AIrEEPA Mep3reKA. r. ra

iH. AKaaeMi,{Hrai

pieexe

illi

zss

2)a=415,x+Oi 289.

y=(r+1\a

CrcreMa Mae qorrp'r

rapr pGB's3rciB.

CEcreMe Ma€ aBi IIapIl po3B'sa1ciB,

290. 1)

l!=*

1"8

287./t.rt=xb.RkuoxtO.'to l(xt= a.

npaoiK OlBKuii cltMPrpxqHxri BinBocso oci

l' l jr 1J rlaoix Qverculi cna,qa€, roMy naii6inr,Ee 3Ea"eEns abvH| ro0ro - /[tJ -' savMeslDoro 3HaqeBs' 'l I' = ltu ^" = on. xqin Ha6yBa.. nxsro r = | z) . r' 2. l(1) = 1. abyHrcqiE Ea6yBa€, ff{rqo r = 1,

Oy. Ha trpoMi)Rlty

"0610

lt, - |l Ou'^*'" rpocrac. rox,ry sanMexne -/ rl / 1l =( 2t6 64. 3HaqeHHn: f, ;) ,-;)

Ha npoMi*c(y Es*6inhme

3HaqeEH':

/(-1) = li

Ha rpoMixir{y [1i +*) ibytrKqin cfla{a€, roMy lrafi6inblt€ sssqenHs: l(1) = 1' a safiMesmoro sHaqeHss OyEKqis He Ha6yBae.

288. f(x) =

t3.

lr 1 -" l;;zl Ovxxnin /(x)1

Ha npoMilxnv

cna-aac. roMv

,(!\ ,r., .'u*"-" ""'""",sa ltzt= ''I II '\3/ "'

'rafi6i,bore

t 2; 1l Oygrrqin /ttt = I "ou*"", roMy Hai6inlrte 1._=-1. 1. f= 'ft z\ (-2)' 8 " rrn.a""-e sEaqeHsn: 11 11- (-1) 3) Ha npoMinrxy {--; -31 Oyrxqig l(rt = 1 cna.qae roMv Hafi6inbr',roro BoHa tse Ha6yBac. a Ha;MeHUe rtse*e'nr, t, 3) . (-1," = +. 2) Ha rpoMixclcy

300

l::::: At'tTEEPA

MepsnrK A, r. ra iH. AxaaeMiqgri piBeHh

CrcreMa Ma€

rplj napn

poBB'ssRiB.

lr '- srrno r < -rL-r'. sR'-qo ,r > -r.

291. l(.r)=l

C*qreMa Mae aBi fiapa po3B's3&is.

2s2. f(x\=

[''r'='' 1-.r-"-1<1s

l-!",x>1.

3sa'renss

3na'reEs.E

(F}'Irrqis cra,qa€ Ea rpoMilriKax: (--; -11; [0; 1]; (1; +-). 3Ha'{eHEs

l:iliii{i:iiil;itl

(DyA&qia Bpocra€, sriqo

, € [0; +-). r€( 1;01.

e (--; -11,

OyEXais spocrae

npoMi}Irlly

[-1;

01.

OylrRqi.n cna,qae, .fiKqo

[.atgi:1i.:llli AITEEPA Mep3reKA. r. ra

iH.

AKaseMi.{Hrn pi8eHb

il{:

3O1

2) {,6T = 3. .r{I'cno 3 e apr{bMernqEnM

t', ro6ro npu r * 0, l(r) = 1 t) f(-2\ < f( 1), roai n - HenapEe qvcnoi seMor{inz Bo; 2) f(-2\ < f(1\, roai r - Br3Haqltrr napEe qncno; 3) fl-2\ < fl-L), aonj, n < roai n alrsHacrru EeMor*{,rsao. a)

2gg.

i3r=81.

x) =

3 He € apnoMerr..rlrrM lropeHeM 4-ro creneEs 3.rl'c"ta 81, 60

514

- \lr5 = 5.2,5

z, 1.6.0s

3OO.

= 5:

1) J0,25 = 0,5;

a) (.,/L)' 3('6)'=18 3 8=13-24=-11;

tlzta = a;

3) vo,0016

f#-m=;='i,

r frJ=-'.

"-rr=

3)rr=3;r=tJ3; 4) x.'= -25,,j' € A (a6o I:e Mae AincE]rx xopeHiB),

ll -

Jrn

8)'

, qei

, qer

8l i

Bqpa3 Ma€ 3Micr, srtnro BHpar MaF

3o2. 1) (J11) = 1li cvMa

' . 8.

106,0

{-@: 8l

rax;

["G*s. [x>0r 3) ra&i

sl (-{/ii)"

| \m = 3, ratr, 6o 3t = 27; 2) V1 =L rall,601>0i13=1i , rl-n = -s, raft, 60 (-3)3 = -27; q 4,Ei =2, rax,60 16 > 0 i 2a = 16; $ 4-16= 2, IIi,60(-16) < 0, a noDrHHo 6yr

lad

il (V?)

b) iF=

6) l5V3/ = 125 3=3?5;

-7;

=7t

I0 = 810:

I €=9=g,

64 8

n,=,n.

- er +rll.t,Eol=l45=9=11; \3 ,r 27 3 3 2r (-VsJ

-rr;

:li:l:.fl

6) tsi.

2ge.

i)=,'

303. 1) (i4B)" = 1s;

[0;9) u (9; +-)

ran;

L gt* 22

(-zJ

ii;;,fl .

zr (Vs) =s:

(-3vl0l = { 3f lo 8l

s, trr,[El".lrt".qe -!2r '""'l.z'=".1

\ {8: ' €)

l'- l' ". lr>Ui Hi;

q\,E)'=-z; ?r

,R.

snpas Ma€ 3Micr,

f"f a*0, ' lr>0: 297. 1) TaE; 2)

3vicr trpx

6) '"irAe- = rovtr). = 'oifi@ -

Hyn'.

BiA

6) 1G - sf, qeil

-siF#=-8iF;=

q\[n'={n=la"=s;

296. 1) J :r, qefi lupas Mae 3Micr, nlllqo .1.>0,ro6rot<0,.1€ ( -; 01. 2) r,F, qefi srpag uae 3Micr, nrrqo t € R. 3) J r', qefi sr{pag -ae 3Micr, nnrqo -r'z> O, t: < 0, ro6ro t = 0. a) Jx-8, aefi B1Ipa5 Mae 3Micr, n&Ijlo t 8>0,ro6ror>8, 1e [8i+-). q JVi, qe* Bllpa3 Mae 3Micr rp't x € ,R, 60.r':? o i I > 0, roMv ixnn

:t o,r.{:on=o,r.V z'.z' =o,E

2) t'=O,49t r=1O,7;

= o,4;

:::a;il*

'; ",62s _ ./s' s so1. n {Ear = "J?" =7: ,,i/trl-\l \l, 3

295.1\x'=25ix=!5;

6in6ua

fo,s66s1=-6,1;

7'4 110,125 = 4. 0,5 = 2t sl i6'=i6i=s;

z=! o.a z= r,gr

+, 1{,,/is) 'rJrn) - t..ta | .rn 6262

105 = 100 000.

foryeMoca ao BxB,{eHBt HoBoiteMtr 2s4-

-3 <

4) qrcno 10 se € aprabMerrqHnM KopeHeM 5'ro crelreHs 3 ql{cna l0 000,60

l(1),

l(2)

KopeseM 4-ro crenelrn s.rncna 81, 60 3 > 0

45=15;

(

r 2r' (J-5) = 32 {

160.

0,3.$[boo-s V25o+o ( '{6)" = o, a . ro - r ' z r 6 6=3-1o+36=2e; 2) Jr4'-t-2Jr0J t t2a='4-t 2t' 10 2 t4-40-2=561

so4. 1)

tria KopeIIeM lapHoro crereEs

HeBia'€MHe wrcro;

a\ {-n

:gi, 60

2' = s2.

299. 1) {6 = 2. rlrcro 2 e apn&MerlI.rHllM Ky6i.{Hr4M kopelreM i3 'rrcra 8, 60 i2-qnc,roEeBiA'€MHe.

302 llt

AnTEEPA Mepsrqx A. r. ra iH. AKaAeMi.rHr,rn piBeHb ii::lliJ::.:.:.::::::i

5/ i\ ? 5 =:t4\ -2l + A+ A

iiiifiiilil:.i:ii

Is t2 a

AITEEPA Mep3neKA. r. ra iH. AKaaeMi{i{ri piBeHb

ii'.1 3o3

sos. r) 200 i6,oor - 5-63oor,

=20+0,2-32= 1<o

zr Veooo.l/zoE ' 81

s3l*

306. 1)

25 =

-\-alz)'

zoo

ztr.t1 {i=-21 .r=-8; 2) ili =-2; "ea; U {i=-2 t=-Bz; \ l,lix z=o; iTi =2; sx=ror r=s];

o,t-{-0,2r-16 2=

11,81

.rr.'oo 8 {ve)"'vrz -20.q 3 r8) 3

rl i6r-z=o 3x. 2=o;3x=z; r=?' 3'

,,r

q lb'

2=2i 3x-2=16iAr=1Atr=6. 312.lr r:3 A2f + 81= 0. Hexafi r.a = t, roAi t, orxe, ri = 81, r = t3; ,a = 1, jr = 11.

5s1.

Vr+6, r+6>0,r>

6.fllcqo.r'€[

+-),

Brrpa3 Mae sMicr.

U to tO. flKolo o = R, ro s,{par Mac aMicr. s\ flE@ -1r, atu - 1)>0. ,finnro y € (--;01 u [1; +-), ro Brrpa3 Ma€ sMicr. t\ !li, y > 0,, < o. sRrrro , € ( -; ol, ro Bvpa3 Ma€ sMicr. 5) V r', x' > 0, x' < O,.r = 0. .flI(a{o r = 0, ro Brpa3 Mae BMicr. , ---\,,--'Plx' -zx - 8, .r, - 2x - 8 zo. flKqo r € (--; -41 u [2; +-), ro Bnpas Ma€ 3Micr. a

T=\t--)/.+

i$ffi i$jgiili

s=4x-2, x 2> o, r> 2,, e t2; +*rt v=!4 t, re n; -----Y-f=\fs) '{2' 4, 2x - f > 0, - > 0, "(2 ")

--\,,--. ;

4) 9 = --_:]-,

llx

4xt4

tc6

+:.t 8, r

Bidnosidb: 2t

jr3

= r, roAi

t'+ t -

. ' '

t0; zt;

(-*; -2)u(-2; +-).

8l=

56 = 0,

0, t = 81 a6o t = 1.

t = 8 a6o r=

7. Orri{e,

.r" 7, x !7.

PJ1

3) ,rr': + rd - 12=0. Hexa;16-t, roAi t2+t r.d=-4,r€ O;t6=3, r = Xeh.

3O7.D

o2 x, 4! +4>0,(t-2),>o,t*2,r€

!3. !1. 56 =0. Hexeii

BiAnoqiAb:

82t +

=0,.=-4a6o t=3.

O,rrie,

I'ldf:rg$

lar5.

BiAnosiAb:

x6 25x3 orxe, r, = -2,,

313,1,

54 = 0. Hexaii = t, .ro(l t2 Pl-z xs 27, x = 3. = = = -Jz;

ffi i:.1{.ii}:r0 ':.:':di.tt$ ::!::::n:.t$

-25!

Biano'iab: -1,E. 3. 2) ,3 + lAx4 - 4a=0. Hexai ra = t, rori r, + 13, r.a=-16,re A:xa=3, t = ):1h-

54=O,t= 2a6ot =27. :;.:riii:rq

48 = 0, t = -16 a6o t = 3. O?:*e,

Bilnoai't t{3. s14.

\,18

a, sxqo a>0; z\,[V

-a,sxqo a so.

4)ta=i6ir.=!2i 5)16=5; r=1{,6; 6)xt= 81tx. At l, l, 7t27xt I Ot27x lt r' * 21' - 3' 8lt.r- 2)J= 125, x-2=5: x=7i 9) (' + 5)1= 10 000; (' + 5)1= 101; '+5=10a6o'+5=-10;'=5a6or=-15. 2) ts = 12; t=!!ltt 309.1.) r'= 1; ,r = 1; 3),r1o=1; r=11; 4)rt3=0;jr=0; 5, 15 = -32: t -- -2,, 6l!6=-64',xeAt

2 0i64r'- 2r'-il /rA''- ,,1 8) (2.r - lf = 8: 2x+l=Ja:2x+1=2.2x=1t 7t64x5

e)(ir-

x=f;1

l/r=:: x=-:-:: 5 125 4) {i= 6; x= 216; 5\ \li=-2; xe a; T {2' +7 = O; {2t = 7i 2, = 44Ai r = 171,5; at \l2t+7 =O;2t +7=ot2x= 7; x= 3,5: g\ lfLrj 7- - 7t 2r + 7 - 343 2r = 336t r = 168.

304

Jr=9: x=81:

ll:i

3) {/x=3: x=81: 6)

{/t=0; r=0;

ATITEEPA Mep3rrK A. r. ra iH. AxaAeMirHur pieexs

2) -o,4.{V

= 0,4c|;

atz.

Jn"=n,

i) JoSl -:o = 0,8

zl ,6oo

q 4\

6 = 4,8;

\1100

3r8. 1) .v6t..8

t-a=\fV2e;

.r-s= -{F, r-3=-3,a:0. '-a=Vtrr "-a=i/F; '-3=3; '=6, 31O. 1)

J;t=bl;

sxr']o n >0; 4 \E6p' = 4p, s&s{o p > o; 5) lf,f, = cu - c':

316.D

s)6= 72e;

31s. 1)

.r52,

,E =)"");

J^"

1F= n, rrxt4o n <o;

.,63e* - -o,or,

^t=^,.

s&rqo & < o;

,!,rr{t - o,stl=

J6'.s'=6

! 36

o,br?, a<o.

e=b4;

,lra Ezr rr 36 6 'l

-s 6

= .rGZ = s;

Jo, re = \Eoo . oJs = .,66 = o;

Jl:.Jt.1i26=,fu.2.%=,Ed = za: E3 tE.s" =tE 4 =2a.32=16 s-r44:

f,Ez=n$=.ao='' t27 /s.3

3 s '' lt+z 'ltqz zt .z.z 7' "lt ii!:.!lfilii:*

i:i!{il!:iiliJ:111

-. vE fs fi

J48 ! 48 V16 -=-l-=,1

r 4

.6 f5 /r "'h.Jt2 -Va ts-Vs

alresPA Mep3rsKA. r. ra it|. AKaaeMiqHlri piaerr

li:i:

gos

r 3. Bracr[Bocri xopeHr n-ro creneHt

{6a.lx=+ s=zo. sl !21o.7" = t.7 = 4.7 = 2a;

319. 1)

I Jni'

,zs.

z) Vo,oezs. s1 =o,s.s=r,r;

i,6" rd'

= 3"

z1 163osr.

,r sl

1!8. +E = 4!G

=zl

,' ll 5'' -r' 5'

Vo,

ora +4 = i6-ozro = o,

25 -72 25

2zz. 25

Vs' . 5' = 98" . 5' = B! . b =

e .5 =

tl2" 7' =:12,"

.,[i-6.

45;

rfr..,,Ao

vior

-t*

= Va =

szz.

fllzi

,,8i/5

= Pls' =

$1- ro Vto'.3,

to-, I0".3" *t' " : ro'

. l0I

al J1%.Jis ,E 323. 1) gZq.

.,.60

tGr3)' = l-1sl=

{-oy =

$[ e,' = -el=

= st":

q lEE"-t' =lr""al - ba'b, 60 a > o i b > o; q ltFzg""W = Ba"bs =Basb', 60 a > o, D > 0. 3OO lrl:ArrEEpA Mep3neKA.

t-.

{a'; ilt';

D lxE =flr)

a\ '4""

o "{"-u = tEi; E=,F =a.

or 987

= Vs" =

"6;

ro6ro d

'i/7;

r) 'Vo'' e I

'.Vf,;.

{d;

'V;;;

'{6'.

ra iH. AxaaeMi,{Hr4t piBer" lfiilillli:l:::i;i

", "=ot

:er. r1 $6

tt .t6"" =lS" =5r,, 60 a>Ot iEtn

{i;

= {,Ar

,t, '9,.' * = i/', 'V*' t/ x

- 0. 2) Vo'; gl 'Vo'; a)

'6.

6) V{o 5f

={tr*8o..rEe'r=1181 . ,1 . ../86 = 5 . 2 . 6 = 60. z1

\E,

n[rE =

:t i,fT a; a q 11"" =

=4,6+n ='4.8=tz:

13.

:so.t) Vo'=o; d: o: zl {a' = -a. a <o:

= 4oi

Jrz = ilst tz =tlu st "/i7 Vg el l,E.,m tn nli"tw -ro - l6a - roo = tf az = -z;

v-"Frr6i=ry

= llo; =

329. Vb, '106'10, € fi.

r[t'.-." \1

sr i/i -

sze. guoo

= I.t7'

VB:

.d-:

s, 4n" er c[6

,l'o = rrG

g dr" .5" .4* ni +r

7r '1/8r '{3'

;uE

=o,+^"n",60m>o,n>o:

2' \kli =,4;. sl '{"W = Xlo'a- ;

z) Vaa = iF = i4;

= s;

tEt.ict =.€. zz i,6.1-ey = 3.1 3y=-e. fi. f'o ro, v35 =,Fm ! 35 rriu . ".

e) x6.VI

= lo,tmun'

.rr VF = {,6t;

-ao - t6i

8) {,G6* 10. {,GG_ro = iG.gI -

=)*"""1= ^6n3, som>0,n>o.

na.4 .ld" ='\G: q 4"" = \E;

]zz.

=2".7 =8.7 =b6i = t,[ zr

n zol

u :Jm"n' t,",, - r^^". F,tr" rF?^ rm n

ela a

6)1::::::

tl,,t"*

rn";

t - V128="[t=,E ^'i !r28 !32 2'

ff=1ff=,.,0'=', 'E'

= 6,3.11 = 3,3,

o, uEl

",8=+=i='i' s21.

rr'

;lf i6,ooooor-

.1s' = 276 996.

a,l

320. 1) i/0,064€43 = o,4.7 = 2,s;

7n -7n.

D {rzs'.-

=11,E-r', o,-s; =lva-5. dcR. o',

o 2 6t

=-a', a<O; 3t Va' = Val , a>o: q dd = {-;' , "<o. a""

ssz. D l,l"t =+6.+lo, o>o,b>o; D <l"b=1 ".11 b. a<o,a<or

4 { ab=X6.Ilj, d>o,}<o; qiffi=rl;.X6. ae R,be R) 5\ XGb = {-;. {j, a e R, b. R.

i:l:lttllJllt:.lj1i UTeSPA Mep3rcKA. r. ra in. Axasemivnrii pieenr

i{f

r-2>0, sss.U lxz -n= dx-z

<Jx+2,

r € [2; +-). s(z xt zl :F - = lE4 lA - r, [(r.-3)(?-x)>0, f3<xs?,

PiBsictE BrxoHy€rr'ca, slirlo

lr 3:0.

lr-r,

lt-"o,

,lrSitfiiji!:tiixli :lt$ri;ir::il*i:J::i

litl#-&i':fli

z>o,

.it 2-

6) 7)

l[; = :;,

l*=t,

l(x+1)(r+2Xx+3)>0, I

", -r, ll*r.0.

l-r+120' lr+2>OI lx+3>oi r

-1.

334. 1) t6{

{68

1v+2>O-

l**rro,

l"'l;

z\ {u-

t €[

3) 6)

t[a- = a"l= "";

'.3G-o"

'3) 9"'

= a";

la'l;

"',

s&qo c €

11 tr6""5 = slt"yl= ax"y, .,6, o1o%F = o, r lo'bul

b < o;

axulo y 2 o;

1,8 5o^ =

rl"' =so';

z) i6, ooorf" = o,r a"l= o,1r', sxuro , > o;

-s.zl" = r0 (-r) = 10r, '1Rqo , < 0; o,ri,fiooo ooo"" = -o,t tolz'l= -z', z>o;

gl -r'[a'"

lal rr.monyerrcs, Frciqo a > 0;

lal sx!{ogy€r6cs,

srtnroo€.a.

rt tf' a=lol-o. a a=2a. ertto a -o; zl \la" +4V - al+a=-'a+a=o, m{qoa<0; l/V =o+

\,[a" +

-1

Jx lla

=lol-

al o.

r) {, +a)n = r + a. Icnoci':lx+4=x+4i ), . -n. J' . -4. I 4=.r+4: l-x L2.r=-si

n. !,. []+4=r+4i l0,r=0;

I,'-

BiAnoqiAb:

t4i +-r.

tr@++f

xe Al:

x>-4.

r+t, {,+qn =lx++=,+t, r > -4. =6-a,f, {6 s,)'=(1-3'f =(1-a,),,

2) i/(1

r 6

3OB l:ij AnfEEpA Mep3neKA. f. ra

iH. AxaAeMi'{Hr,ti piEeHb

-,E)' = Jh - .,8 = J-r + Jz. = q/.8

i/("8 "5I

4')

i/rJe z)' = Vl"6 -

= -.o,ta'ou ,

*,'la:.,,-:=*;' = 4*+, " . -f;.o,o.0.o. ssz.t\

)

rar.rl i/(G-z)"=J"6-rl - n/Jo -2. oo Jo '2,

sriqoa<0,0>o; s) -1,2*,h4x' = -r,zr,.al,u =-g,or'( r')-9,6ru, s&qor<0; el

flxqo a € E,60 HepiBgicrl o <

qe Mo)rirnBo, gl{rqo

.R;

o,sla']= o,5r?, sriqo

a > 0, 60 EepiEnicrs a

""o"ia: nnllle snu]o ir + 4 > 0, zy X{r-r'y

{zsen" =zpl=-zn, sKtr{o}<0;

16-zra'

< Sf,'.,

=1,-51.

= 2&t-- 2p, snqo p > oi

B\ \,@ =b'l=

i6t > l/Ft sxqo

4 (-n,)k'

4m"

310.

t {/aru = rnl - rn. qxqo rn 2 oi zt !r^ = nl= -n. rxqo n < o: {t6p'

-1

1; +-).

\256n'

h>O.

-2

z1 -0,+{V = -o,t "l: l,[iF = n":

= lbl;

33s. 1) 1,2rV:0 = L2l*; q'{@-0- = a-v. 336.

PiBEsIrHs BljKoHy€r6cs, st(qo

p'q', srrqop>o;

=1n"nl= l-^").(-n") = n"o", .aftqo m < 0, n s 0; ab' 1t7*b"%4 = ab' .la"b'c\t - ab2 . o1, bs . ec),, = ata"cn, s&!ro 6 > 0, c < 0; -qfr" . "E-" !: - -an'p" .'h"tlpot 8n'p" k'6 pto -"P -o^,"1.. ^'

sss.

t('-a {"-a),

[l-a<*<

= lpuq'l=

'tr;**

338. 1)

t € [3; 71. {6 r0, : e R;

s) XG- 6X' - 10) = {,6-. 4) i/i;1x,+2X'+3) =tt,.U

'{6*q'

m <O,

3<,rt?.

PiBnicrr, BnKoEyerbcs, sErqo

r ti::iiii'-{.}:.:.::j:

x+2>0, l"r+2:0, a> r' - 4>o;

s+2.

fl(,6 -

z)'

oo ,E

-,6r

JJs

J5 *

- zl =

z. oo Js .

2. 60 ..6 > 2l

zr V(G -.,4)'-- = {'va ,al = 1tfu ar ((Jrr-a)" =dlJrr a = {Jrt -s.

-i6=.

,,5.

Js:

JiJ,B;

t;"r4) '{{J? - 3J = VJ? - s.

:iill:iiliil:iit: AITEEPA Mep3nrKA. r. ra iH. A(aAeMiyHrn

piBeHb

fl.!

3O9

3a3.D s=a,,8

-x= xl-r=

= x- t= 2t, fiRqo t

3aa.

s=2r+\[ru =2x+ xl; a)r>O,U=gtt 6)tc<o,a=2r x=r; z1

< 0;

!={V

2ra=d=.d-r"-dj=

=lx -2x.

g&qor>0, toy=r 2x= x; s&qor< 0, aoi=-x 2t=-3t'

t) v=Ji {'" =d"' =',

q y={1' zf =,-z;

r.>o;

flriE{ot<0,ro6roy=-1.

t/,"h

6) U=-=-.

OA3:

+ 0.

sKrqo

< 0, ro

.fKrr{on>0,roy=1; J,

-1.

2r'{f =6 h lo-r>0. Ilr<0. I rno.i6: I lxl=e-x; lr=0-

3a5.*lV=r-a. sr

.y',' V*'

= lr.l'? xL' = lx ;

u=fr.2=fi,2.

OA3: .t * 0.

s=4+z=i+2, t> 0, ',=!a2= f +2, x <0;

lr-4>0. lr>a[l:r =x-+: lx=x reA.

t>4, +;

O-t=

f1* s

,>0.

iF.

J"'

vl' .JI

J, l'r ''. ,

10..r

!'=o-,,

l-=

l'=:

lr+3>o=r+3r l ". l2xl=r+3i l2lx =x+3;

BiAnMiAb: ::::::

AtIf EEPA Mep3rcK A. r. ra

iH. AKaAeMiqHr4f piBeHb l::::ii:+:::i:::::::::l

lJ0 < r s

[1"=:,

cnoci6:

-lt

s,r

J-3sr.so, l-2x=t+3;

I-3

I',0,

l>o,

[2r=n+3:

s o.

BtAro6;ab: pos!'s3RiB HeMa€.

3) 2Vx"

[1'

ll-'=o-": llo,=e, .t II

zr y =

s o,

ll-ss,cso' f1-s<'-' o. llr=-a; J,,0. l)x=x+a: Io.t-8;

l"r+8>0. l.r> e, )r-.r-ar llx '-a: lr '-a:11"0.

!F=x+a;

3a6. 1y

BiAnosiAb:

2t Vr"

-5

f6'-10>0.

r0: l

lJrl=

6.t

10;

r=6r-10;

$.i!:;i::::.{.::::$

1l$z:r.tl$

jiii,ti,yr,Lidri:il ,:q

"!.11:.:.:..1:.1:.: - 1 :!:i.:+:.r.t

5 xl=2. r Bacrocy€Mo Meroa i'r"n"-i", ftQfi ir<,q lr< j. [*.3,r=s; tt1,,*t-u-' 2: {-zx- e: l*=a' l"r5, l2ir =

y = 1,@ + rf

*1[:-F

),r,, ".a. I.t = 5;

lr - sl.

+1+

CilNE:'=-

ar 350.

3145

S"Eoo=fr r)

316 = 2"6;

ro"E=.E'

aJ13 = ."6.rs =

d1?;

a) e .,6 = ."66d;

312

t62 +

= a. zJz +

'la

nJE

+ 27 =

- tzJs.

)=,rv,,,r,,r,

)Jna=)alz=+Jz:

4J -o,o5G4oo =

zl -roJil

4t -;J54

= l;

-o,oo

-'4a. ioo

lJi - Ji)(J' , "rt)

,lb

Ja + Jb

^. "E-t Jz-t r JI3' J6 J3 J5(v6-t Js .. Ji5 '6 v6(G-€) J5 vit ' b J1o G(,6-Jz) ,6 5' -. ra ,45 ,/iT(,/i5-r) o, +=vlit-t: ./13 v13

e.,E -

^. "*2"!oa -= o,

-Jlaoo;

aa+ali aG*'6) = 4 -. -;r = - 5 G - JF)Ta + G)- ;Gr " -=-+.=!a+JD:

J24.

+,lb

Vd + Jb

r,li

_ "li '6 (J;)'*(.6I ("!;.Ja\(,E ,t.o -

^tr)

-l;;tF'

u@I.ffi*a =.[7-ro =r; a (\ffiG $ - 2.,6)' = * zG - 2,,(o * z^,6)(6 - 2;4 * 6 ru5 -

sss.ry -,ELL= = zsJt;

s,!z = e'E + a',8 - sJ, = tt"E.

li{: AIrEEPA MepsIqKA. f. ra iB. AKaaeMieHxf piEeHb

,la

+a Ui * Ji\"

ro.zJrr -Jrr.

gsr. r) uqb - oJ5 = s'6 - 4"6 = -."6; zl r,/iz - z.',6 = ro"6 - z.'6 = 4"6; el ali,-tuT+zude=s 6\E - a"E +2 7\E = BlE - a'J,+tttE 4) 8.,6 + .,[ 2s -

fr=@jp=6.,,

".o.'r

foryeMoca rlo BxsqeHHi HoaoiteM]l

34e. 1)

2 (Jrs - J12)(Jr5 ^___!_rr,_5r-(/,.##;='u(fl;f Ji *16 Ji t Ja Jb=ltE - ,tE)(J; - .tE) - "ti

BLpaBiB:

x-3=2t;

"r;

(a,6)'

rs(,,!B*"/iZ) :=-:icq{

r - 1=0,.r= -1 i jr 3 = 0,.r= 3. fitrqo r ! 1,roy=-, 1-x+3=-2r+2. 2x + 2, t s l. OT)+ie. fl&nlo -1 ^' < t < 3, ro t = t + 1 + (-r) + 3 = 4. Orxe, Y, = 4, -1 <t<3. gr{qo t > 3,'roU=x +l + OTir|e, As= 2E - 2' t > 3.

s."i5l' = (-z * su6)' = a - z. z. aJ5 *

10:

SsaiAeMo nyni riAMoAytr,Er'tx

iJ")'l= a -

*= L2f,6- =rJ6, J6 J6 J6

BiAnoaiAb:l,el3i5\.

ale.

l;l=lJbf

lz JrkE-r) $Ur-n ^.E;=@;t(!trt= ,-1

I3"t5's.*<s, ''", J3.xs5, lx-3+5-x=2: 10.r=0r 5+x=2:

= s,

24 zals a"6 -zt-=-=5J3 5 J3. J3 5

=2t x-sl+

{"-#'iF-'f

3){ '[r-3

at lb - ,t;1. lb

sss.rr

Lr=21

G = -,81. ,6

iz-,6.1'6+r =(z-€).(,6*il=z.f +z-a-"6= 16-r

l-.1,

BiAnosiAb:2.

erz.

-4.

= 6ir

3s2. 1) .,6 - ./1t1../6 = 1.'6 - z.'6l

2.,Q6jl =12 z. Jte =n-a= t iifli$illjtif AITEEPA MepsrsK A. r. ra iH. AKaaeMiqHnt piBeHb }i:!: st3 = 12

ss6. 1)

=C;;

!,:-"

2\ \Eo" a,

oJi+u = o"

z,"lJy

Jim

q uG'V 357.

mJi

=l^^lJn=^'Jn; ualu$ = a't6 ,rG = a"b6.tE,

-zx"Js.

:or.rr ]*ro=]r,6" r =!.au"ls={s; 2l 2lV=\Et=./16.7=^EA;

a+0;

=sl'1v'1J5" = -slx v'nE;

-.hn', n>oi

sxs1.t6;'

2) sn.,$

o, a < o'

al prT = uF, p>o;

t>o,

1.t86

ilt-

<Er],a" =

l[e.6 n"

=11

"-"

= z":tli""

sae

-r,z16e

360. 1) 160 = i[6 '5

*,&s6

=l/t

3=-t2

21JE

=.,/ir;

+ 2a,6

4) s&6 216

- 8!b = o. +

8V5 :i6

l I

= oi,6+ 0i,6.

-ztrE

-li i::i::i.fl .^. --

+7!b -ar,tE = a\E,.

-vi35 r1+o=i6'

s 12".s-i6'.s

ii:::::IJl

92".5,

iii:::ii{N

i::ii:ii*l

= t[q.B =

;

{Vsa = Vbai

7tblab dt-w .Ja,,",

i,fula

= .il14G

6r y2vrv2 -

b,'ltE; zt

soe.

t{8={q"i=\6at=I'b2f;

3) r0f0.27r -fio'o:zr= rDzro, o,!ut, iffii /*, 6, 2{6v = ilniv = illeul o ulloa' = lEzs ont, =:,!ii; 314 iii: AIrEEPA

V320

*e&E;

6!b

,{{F =\F = \ti, a > o; at tEtE = tl:[t ="4u, t>o;

1Al

z'tuB

V3V2 =

s, 1{;$

;

2.,6 =

z = s'Jz,

16o ooo ooo =

sor. r)

-2,4\b.

216;

tot6; b\ =1P zo" =s u"W' 3 et {6Jsa""' IE Bb' b ,'"

rt s.t6--z{6={f,t

saz.\.lzJs =

2€=sV6-;

u Jin = "ul7 t"

stG = z<[i;

soo.r) VEa si46+svi28+{t000 - BrrE s.24r+s.4(t= = BltE 6{, + 201,8 = 27tr8t zl i6fii +eXE6a z+,EG + t4tzgu = s{i * a<,li - e+ri a<[i+t z.ziE= = 111,G - 6{; + 24!!E = 2sd; .

|t[i ] rtz xE

3i[

ztE=ri,6-al6 16=o, zl {san + :!-td ; {-an - t,s\lian + +lq+s* = = ztFi - strFi + a1,E; - 1, E. 2{ sn + a\Fi = B1fti + o = s4lii.

o"11;'

1,2{2"

363. 1) ai6 +

=stJi

sss.,,-tvto = f,slz= z"Jz, a *1640=;ic€2 5 =i\tT-=!r$=;lE, f

36s.r) t/625

7:) d-b4aw = lt n . rd av = -zot"ttz""-; s\ { !o8a,b- - t[-n. 4d'. a. b" . b = -s,a"o'{aab.

=18i7;

so+.

:''fl.o,

.too"*

:y r{,6+aV--{,f, +rplV =sr!;

zl +En = a,Ezs z =t<,E; U tEu - +lza = s+tz; s;

lEsn

n<o;

= 2\El

o fzzgo l/i' ro

a >o.

4. ToroxHi neperBopeHHq Bllpa3iB, tKi Micrqrb KopeFi n-ro creneHt

3se-1\

+Ezr. +" = +E:r,o":

4) o,BltrooV =

= JsVi = n[in",

4) lalxn=W,

rdG -

t,"{i-{X

Vfo

Mep3neK A. f. ra iH. AKa.qeMi'{Hnn pigesu ::*:ili:!i:iJl:il:j

='i;t

VTE

.77,

W,rze = vrze.

lojo vi," - il," , ' o,

\kn = \,ln, s) i,6.,6 = {,F ='3F, b > o; zt

ula,f,a =

xF6 = flW

V''V,' = Jq/r'

fi-,/"v,

.e/,

=.Vc

{6, .

" = V",c',

> o;

r'o;

r/F=v"c. (/,c-vf,

i:ii:iiitiit{il: AI|EEPA Mep3rrK

{a.={a. a

A. r. ra iH. AKaaeMiqHrt piBeHb

ril:l: 315

sos. ry (r + Va zr (r

{fr)h - la)= r - ",

*,6Xr. l6Xr

"6)

= (r

* G)(r -

â&#x201A;Ź)

-..

(G *'[i) (di. {t)(et . et)(.v6i - pl;) = (G . J;)(<,r; . i6)(i; - {t) =(G + J;)(G -J;)= n-n; zt (l; - tri - !o)\{; . = J; - li.

az o.

37a. t t

n .fo

Iil! :i : ::::::l::!t:-{

iili::4:.:l:*lil: :

:;r:.i!t:.!:

"17

J; t6=flF

c'E .. vz\,r r,

-y'0-

:lt

p!;a t!!A /o d t !z !r - ,,lz rJz. e,

-de,

V"/"

V" =

p,Et"

Vi6;

vlnr .

Vl_d

a > o. b

siEG - i[ooo

=10+3-10=3;

(2{E

+ 3V32

- 2(/108) = Vt - 3i/0,25 3, -

2{6 + {/ioo)(Vio *

Va-) =

ro n e =

olEz + zi/rrzs 16 - 6.2{6 + 2.516 4\ 16 -

-----------il

316

fil: AIITEEPA Mep3nqK A. r. ra

V6l

r.'6

-z

vzz r Vi2s ttz+a *

-f; s _ a"6.

=s_

4G:3E-

s/f

g.s " z,

zJa + Ja - E"E

aJ6

- 4,6

Var.,6".s_rVe _!r -s'-t'

Vs' e J=ra

4"'b"

6;-;

2ir-?

s. z*

j -ftiT -g t {F -tr^. a ,'etr=-;=n"<|n". n'<,ln"

(2.'6 = .,,6. s = Vao);

-1-12+10=

iH. AKaAeMi,{Hnl

pieenu li{:iiii{:i:i{ri{:i

r/n.=FF

ffi=#=',f

_r"iG_

roy

s.6 - r0

szo.

_ z"lz_. tlz.

*=S=l!@=ura, {/8 V16 2

4 4 z' r2f!l . = -4i6r; -3

., = Jl!!V(-3) VB t/3. ^LL

"fl|5t" =l7o", r>0, a>0. (r14 + o,rq/ios - {.600)*E = r+6+

6)'V8 +=l!SV8 8'

'{"+ '{'t" ='{"'a" '{A qW =4"w 4}b"

2) Vo.2s{V4

- 3J6

_ ,E v5 qF iF ^Ei .E brEF=rF'F=vtr=ls'

4,,ia

=:["'a"l

. "G.1t;=llF.{x.{i={"", ">o; n, E=E='$."'0,

azs.

tV24

_ ,, V4 | =46 V64

16 =

at t["+

;

td;-

%''"_' ,t1 =,F. {a"a" 'lano' ! b 'l b s72.1\ {; lE='{'".'{7 ='17, ,>o; ,t ,ly' . do' ='dr" fr ='il6 = ttr,

Job

'{"* ='{."b" 'fao' 'W =,{'w =XFt,

n, t/o'a'Voa' -

""Jr-EtPp

.rs.r,'Vs l=t@

'ff V" +17 ,lo - dJ; o z o: f,-=vlg=d*=ra, .'19'v9'v3.'v3. '@ "'@

"l'" ifr, a > o,

{f'0. o>o,b>o; B) {1; '.i6 ='d'"...v''' ="!^oo", n>0,^>o; ,!4 o, =,4V = r1;. o , o. Vo =,{"_ 'Xa" 2\

r ll :;,! ::::::l:::::::

2 - r"Js, 51i,

-4 3 2-9.3+5.2= 24=9+10=t5+10=25;

'.ta)

gzr.

Ia{?

".o,

=,ina,

(G.

v*'

r':-!Et::!j =tEt. -ii-9-, a+o V(d+tf

=1$

ft=f

=nvs,

=z<8,

., lo - {hooo= vroo: ,--^ vro- -v-i o

,,1.

i:l:::l::ltiiltl

ttu,

#.roJr:.l' =:tzs,

n, -rs _ rsVzz'

ll27

24=

,<li=otts

sVa" b.s'V3 _../".

27 I z+{te, s.z"dz ::r-;"

t;" xf'

= rroE,

=m.d;. n

.o.

AITEEPA Mep3rcKA, r. ra ifl. aKaneMieHhi piaexr

!:iil grZ

vb) szz.ttN!-j=t@Lr,_JJ -{{6-vbrlq

..i1,

'6.a 0.4 o,

szg.

q l'/,- rlln' 3) v, r. ,, , o, 'Vr+3 'Jx+3 r,6,t/'" r) 6'' .^.o, -' ^.G,li \l^" lF(.f'" r) ','(.fi t) ^ ,. ,t*, ."1"_! d"tlf, -,[x\ q,a{i6 -v,) -"J;r, " ,totfa "' rr,F t;6 'tlub +

,,,,\f Vr, -

avr

G-

Jrl,f _ (V,

a)11tr

oi a

Vr -a

re)

(la - va)(r,6 - Vaa + Vo) =96+{a, 1,la - "Jat + {a

Ji {'t {t jE_ lE(.4 r) =x? ,n, z rJ2 :12 *

.-, "^.

12)

',8 r

,,G

3ai. 1) i/a'D: = abi6E, a >o, b >D: zt +lo't = ollt, a > o, 6 > o;

)

(",

J;("6

("6

- r)

tf+t ':-: ' Vo I

:li +t

4;-fi= o,

(V,

-'l;) tt;

Vo)(@1.

jg!:141

t'b

m'O,n>O,mxni

={n

*l,toa*tr|t",

olo ali -.t*(J," -Jt) - Jo -Ja. , o.a ..lab

Joa 1 rlii r6(i6.1) :: 5r -i + tli :--b' tla"t:' + va,t Va'b(1+ Vbl ndD 6)

6J"- = ra6-6=O=v;' a-b

Va+1

(R/a r)(V, rl vo

J;, x6; Gll;

!(i6.!

"t(G

a>O, 3za. 1)

o't,

Lo'Oib/oi

sLr,3 vgql--! i/27,r. \i3

318 ltt

,,,.

. "11'0. lo I 'l Trf.-'r, 11 Vtoo-Jrorr -"=.27.. rl(g. * aVr vE5l n, ),-o,r(s ra{6-uus). =.lg3d5'V25) tr 3 - V5 (3 - V5l(9 3V5 r (/25)

":'o,a:'o;

(1, -

./r. -. Vr8 - "Js /a(verr)-Vt' "'EIE={,8(v6.1)

'l'" -rt'

q[t * i,6t). 1r =1 == (if' d+b la+lb zlvs - {sr v63 rv49- g 7vz) . ","

V4{Vt6 v4,1r

3so.

11.

,,rV-.

t(f '.{o) l,16*oa), ----!s+4 9'' !2s-t2o+t16 slJro -1./r -r) Vra V[*t A, b _ s 2 "J2 {\tla - t) :lz1t . t1 Jz

,t"Hr" -rt'uy'-*t) .r/o-ra. o o.a

,4.a

"6:

tr o>0,b>0;

116($* $) '{6('it -'.i6)

z- (lDE * Jis * '-"; ";" "61 '-'= "{zs {4s

15 rs(,6-r)_.,"6_,,. 3, - V:o r{/o t o

.,/i -

^. tE ,'{oa

^. *',.2 2r

{. :l; tE \l^ :r ,n>o.n>o.m.ni ", '' L^-Jn tv,'l -'6)(v,zr-v,) Vln rV'

(vt)' vt * r rr V2+1 =!+-l,Ett. =r = ("8).*r, 3'

AITEEPA Mep3rer< a. r. ra iH' AKaaeMi'{Hrr pieeHt il::li!li:!!:::iid

+lo^o

o16, d<0,b>0;

n<o' = nld;=n"d;, il;trn -la,l. * 4,li = tlb = ,Lb"{b. a > o, b >o; "'lb" 3) ![11 = ,t blflE =, sflE,x+o; q lEz^'w = t,!i . z*'" . *, . . = z. n z^' "'" " ",ltli^% = "' W;, sl tlten'tw = z a"""t"J2=-\atd,tE,c<o,a>o; ")lt"lb"l,ti = 6) lJtrW = {a," a'. b"- b" =l,,llr.lt[%,=lb,{6%.; a >0, D> 0i 7r 4i*u* =11;".*u. u" - a" b"l{ ab" = a"b"d_ah,, a <o. .D +[-n" = \[-n n"

=d2\2-'."' =z"du" = zalfia', a<o; zl d-ezs"' - d-s^ . - = s {i - ra4[i, o.o. "' " st PIdf =lat{"t="apJ"t, a<o,b<o; q :["^t* = r,'" :lo+ = o"lr'"1:["+ = asbsP{a'zb, a > 0, b > o. ""

sss-D $za"

3a4-D

a!!E = 4f2a',

zt,nl\ a"b' i, :i{itiiliiilti:

a>0,

t-",h

{aa\".a,o.b.0; t"",,.', \ o"h'

AITEEPA Mep3nrK A. f. ra iH. AKaaeMi.rHrt piBeflb .t:a:ii 319

,,[Y f

nnlI 1*=\l-lntn' *=lmnl

4) be6 = 96b", D > o, a6o 5) a!-a=-ll-a?,a<O:

-iGf

at6t, = _l}t,. "t' = dVt", t < 0. 38s. r) c&6 = -t6c', c <o: 2\ a{i =d7' a>o; s\ abd6 = !t6a'b', a<o,b>oi qt awl l= = piei ". =. Vro,a,. , o, \ld'0" \ a D' g a1[4 =-d4, a<o-

i6-t.&[el;6

!fuIo

frt.-tr.E flilF

= =

i6or -

{,Gs

geo = r;

{i+-a.ls 'E"b.,={;;-"T'

={u B)

3' ft;ffi

iTs.$srBG

= 184" .8"

+lV

v1?:6110

=*Et-aTs a6;8E,+= {i76-s:o = dzra = +lte" = "ha =s;

rfiE.'{61 - &tr ='61. 8'4l''i6-ffi ='vtrj- {5 = .ooo r: - ,So-r q .F+iTz. Ja -{z = {dAf 5 ;a= ffi;ll."tl tc-E = - t{z = <FF= n6 Jt - ETz = 4c6 rilzr 4 = 1ll. 4 = = $* ta{z "E

=i,FjF('*G)

= {F

-lG iG;tr3I = {i

-iTs 1,E;i; aG =

={as-a8=ti

zt Jua-i tEs.qJ6 = t/(z,G t)' {zs+aJo ={24+r-4Jb

i/25 ' 4J6

Va;

z"u

" )l, t to -

{b" if

do"

'"6"

<li

) = ",tb

"J".

<li'

t|i *:lV -"-

"lt"

**E;*J""

vilil

llt" , {t" **[a" *El7 Va+t[

tlt *<li

16 *

?,t;

roroxHi neperBopcsFr srpa3iB:

24bc

-2{V

itr lF (i6-*6XVa+V.)rvD-ic: ValF=- va v" "n... ^ {tr {,t (,.6-.[)(,6.r./i) ""-;; ';"'-]!=l/b-{':

' "{fr.*[ a-b 6) tla'-!a't -----------Ftl"t'

('a

xtr

-\Ei <li * <lt"

:,1"t kE *

b-" (i/t .l;)(tF.+Wt,lV) 'F J"' (Vb v")R/b if,l 2. B!&osyâ&#x201A;ŹMo Airo y Ayr{(ax:

=2. <,E*

BH'(oHycMo

Vb"(rt. i6) ({,6 . {6f

. +,E

-+6

(V, -a)(,6-r) V,a s -:= -s ,'v" Va r = t#-t(V;-3q/-r) aV" -s-(16 -r(J, -3V,,el . (tG - s voa s) _ Vo - qf,t "v" (vo Vat. (fi ' a)(V' - sv" , s) G'zz ,E zt v" (v, ,.6) ,,_. " ,G - zt "'""; 6 --G-n -'"

\F -iFz

+tr"t

,, | " G ^ -@- - -l -'.I Va' + zVac * V.' Va' - V.'

='{Tb.

sez. D

-'"G*tE

atlb

",Go

ffi-n'61-8G='@-T'tm-;m=

=,tr

iJ;

-<,F,tl"t <li * {t

Vt+r=15-l a, (Vo + VDI V,"lt\ .. "G+zz ( +G-z Voa gl - t/a: ' {;-"tE l"G.ze,G s Jarzz)-

.ii')o-l;J"

va tlb

y*Ei *Jt"

^ .'.

\FEd

v,,

. l,'-xF \1" rb)({x - tln -t[t') lo -+EEtt[x (Vo - Va)(V, + Va) Ja 'lb t" 'tlt (v" t'h '6r------ "6)\+G -to) -" +F

< o;

386. 1)

v, {6JIrf.,t

(<l;

:l11, - rl ,0,

t1a' 111'

-.6)

.6XG - lb). l,F (d"'

@)'

li *:li 4;4i

',lio, (.,tr

- JiJktr.

4ao

"6) 6;4;= ktr \E)(xF ttF)

r) (v'-r)' j,G {"J'=-1) -#. {t:AE:tl1"6r!t q/r (Vx-tl(V.r+t)(Vx t)

32o

lG-1

'.tlil

-r

AITEEPA Mep3ntx A. r' ra iH. AKaaeMiqHri piBetb llf;:i-:I':li!:!::1

;{iili.li'iltli

AITEEPA Mep3rcKA. r. ra iH. AxaAeMiqHrr piBeBb

fl:l

321

Ji.t. Rr r)ii V. --F- ,I tVr t Vr , Vr 2v' .l_.Err (,ar'I = (l/;- Jtt)(.v!:4 G.t

--- 1r I I

0'6-ro-rii(o,r, ro)'{o,a

ro)'-(e,[l- lo) ,,. -si/(a,l 'rol(e,a zo - : . z1G.fe * ro * a . ,i6.fa * 10 "', zo o(.utoGrro-ffi ro)=,., )c' + 6t - 20 = O, x' - 2r, + 2t 4a + lfut - 20 = O, x,('c 2) + 2x(f, - 2) + 10(' 2) = 0, (t 2)G'+ 2r + 10) = 0, x 2=O, x=2 a6o rc, + 2, + l0 = 0. PiBHsllHs rz + 2r. + 10 = 0 He Ma€ I{opeHiB, oo 4=r tO=-g<0.

389.

'(,t*r)"F

*u"*o, 6*1 tx

J' *1. Toro*{nicrr,

rparrnL'a.

ro)

o'*",

.,6'6 - ro =

= 2. qrc

'Gfu

paqioHanLse

q'cro.

*o i,)O-ra,Z'v'ZO r+.2 q. ,qoBeaeHHs. ne""t i6o * r.r"E r So - l+'E = x. rliaE€ceMo ao Hy6a o6nasi

391.,iloepcr u,

-1trr,(V;-r,6)= =# q-E Va-Va

({n *r4Jt. {n 14rE)" =,"' 20 + r4,8 + 20 ra.E * si,(zo n ra.fz)(zo rrf,z) ({60;lt$. ijEo tE) =',, 40 + 3V400 3s2.x=f.,40+ 6x=J.3, jr3 6' 40=0, ,3 4r' + 4a' 16r+ 10r-40=0, |@ 4\+4:t(t-1) +10(x 4)=0, @ 4)(r'+ 4r+ 10) = 0, r-4=0, x=4a6ox2+4x+ 10 = 0. IIe piBEEEHT He Ma€ riopeull, oo 4 = a ro = o. o. 4 o,*.. 1E ttA po . u,E = 4. roro,$nic16 roBe FHo. ([pr poBs'sByBaEHi BaBAaHb N 390 i N& 391 Mor{Ha Br.iKopscroByBaru OopMynrj

:la\' tvo i6l{V: f) = ,, - Vr. {i6 - {6XeG - c,6) t/d - t/b r:t"

lluu*o,

+S = 96+Va.

qac-

toro:rcsicru opanr.'m'a'

tE ua ^ | va - ga r (Va '6')l .'vo--d,^ t'lffi G u,' -'1t ,li:Jt' df,'la ('16 i,)' r (.,/a V,l -ilG)(t;y; 'lo '6 r6ira ' J"-Ju \{;.,bi' ""6k1" 'rE) - +G !t, "ld -;,tb li la - Jo ' 1,6b --iv"-!bl"

(a +

b)3

= a'

+ 1a'b + \ab' +

b3 a6o

(a + b\x = a3 + 3aD(o + 6) +

b3.)

rlJ,,["

,!ot--

va{Jo 16l iy"'vor' ,,a

V,(l6,la) -l;:T

trn -yrr

y=Jt. r; y=]o,re =o,a; a = uE,u =t,z; y=uEooo =oo; jl' z1 o,z=.,E, '=o,o+ 5.=\l;, r = 25; 12o = .,E, = 14 400; -q= G, xe 393. y=G. s92.

".'c'

l!'b "l'b (v,-vb)v" 't-' vb

To.o)r{urcl6 npaBun6Ha.

i,[l;E + iE] 5.8 . :r,u*uii * ,5^f2 t lli - 5{2 = ,. r*' (i,[*rO-if GE)'=", ,. r,E 'r.'E,rJrl {t ,'Et , ti/G. *rrtt turt z tJz

gso.

r+or 1-ry (1fi * s./z - iit - 5it)= '", t4 3,=f,f+* t4=o,t2 2"+2f 4x+7' l4=o'a'z(x-2)+2x(x (r 2\(r'z + 2r + 7) = O, t = 2 a6o * + %c + 7 = O. PiBEsIlIrs r'+ 2t+ ? = 0 He Ms€ xopeHis, 60 2=1-?= 6<0' o,*", iF ti"E n fi - sJi = 2. r{uc,T o 2 paqioHa-'rr,He 'lr-rc'!o' - ro i,6.'fa ro. n",.* 16'6* 10 i/aG- = '. a

L\ A(16:

4), ./te = a, ran. fpsoiK OyErcqii npoxoAurr, repee rovny

2) B(49;

-'lr,

,". 2\+7oc 2\=0'

"no.

a. r. ra

iH. AKaaeMi'rHr4i

piBett iiiili:ilitl'iii'i1

r' .E' E !3 '{5

,4.

He npoxoairB qepe3 ro.Jl{v B. "i.IpaOiK OyHKqiI o, si. IpaOiIl OyHxrrii He rpoloanrB qepe3 ro.rRy C.

"i.

rpaoik Syn&qii

"ls,

He npoxoaurb .repe3 roqXy

'm;

s).,65.6=.,66;

"85; st ,Eo , zJi = Jn; .,.,8=,F,i.r =ff=a. s"E =

395. 1) 2)

',t4: NlfEEPAMep3nqK

"6=

0,6), .v6,0 = O, 4) D( 36t 6), .faO = e, 3) C(S,6i

'6.,E

g22

fory€Moca Ao Bl,tBqeHHr HoaoiTeMlt

"Ei

lu6 +]= "6*+;

J{J2-r)'=l/6

il r5 al .,6*a-.8-e 12.

i:i::ir:iii:::irl::i: AITEEPA Mep3ncKA. r. ra iH. AKaaeMi.{H,fi piaens

!:!lt

323

2) v, = ',li; v"=

396. 1) qE=-:c-1; Y'=./1; A2=

-x

\ a=illl+2, E(v\=[2; +*)) 4 v=di--+, Ets) =t-4: +-rt 3\ v ={; -2, -a(y) = ( *; +*).

4O2-

x..

4o3. 1),finqo 1<

<216, ro 1< Vr < 6; <2.

2l-72s<'<8, s<{; 4o4. 1)O<r<256, O<

i6s4;

2) 16

<.'

< 10 000,

2<i,t<10.

aos. 1) Bi]no6i0b:1.

EtAno8tAb. poaB's3KiB lreMa€.

li$ffi

i,/i- > i,/i;; D 'tl-n > rJ z6;

3\ 2 tlU-; " 4) l,6..@t. 6. {6

,E=!;

v, =

'l;t 1 A,=; BiAnoBiAb:

3)jC'{10 000; Ol,EI{aii ryo,(oalIrL 'rep$ ro'rRu: B(1g; 2)i E(81;

10)

D l I

y lG.

fpa$rts avuk(ii

npoxoaxl6 'reoeJ roekt{:

s; 4; B(*;;); r( looo;-10). 399. t) y l,G. t. aryr R: \ g = alx +1,, + 1 >O, t> -1, r(Y) =t 1; +-)i r:-, x -2'O.x/-2'Dtut t -: 2r-'{ 2: r-)' Srq-:i'-1. t}rr - ---\,--- Y 2>o, a1 y=18 -1 !, [2; +-), D(y) = ( -; -11u [2; +-) r € (--; -11 "-2,""-t D

+13

-/1:r3

;(i

vs a -

D(i

4o9. 1) 4

--\7-

ffi, +Er.

\tr

',X16

"XEGI

tT z

i ii{;0. qi,li

tT,"l

=fo

ooo.oprz ={rzo.

47<4s<2i

3) 2<1/21 <3;

5) -2

v30 < -1;

2) s<{/isg<4;

5<-ve1

3) -6 < -V212

-5.

qrcna, p$rarroBaHi Mi}li HuMI,: 5j

2) iFSs i {640. Ilird q'cna, posrarxoBarii Mi,x Hr.rMt,^t 2; It Ot li 2; Bt 4i

alo.Ilini

qrcna, posrauroBaHi

1;2;3.

= Rl

Mi}Ii'rrcraM[ ,/iS00 i iAo' 6t Et -4; 2t r;0i

a11.1) {6=i66>G=V2?;

l^ y=r/'-^.,r -3, O.x'3- Dlat=t -:3t 13: -): q v =\rF t"+5, '': 4r. + 3 > 0, D(y) = (--; 1l u [3; +*).

2) V12 ='.V144 > 96 ='{A%;

V3 =,V2?

V2Jz = VJ28 = 92sl

q tl'ln =:,tii , ttr = = tE; "E

y=(/'+L E(y)= [1; +-); 4 a = \,G 2, E(a\ = e*i zli $ v=li-s, n@1=P.

4o1.1)

MTEEPA Mep3rqK A. r. ra

XE =

3r srfa = !27 Vros . a'E q E!0,2 = {62s4,2=$zs >ro{o,orz

408. 1) 2<v18<S;

ri::!:

{za

4) 4<V100<5;

g=\E'x,2-t>O,t<2,D( =( -;2lt

324

4o7.D1<J3<21

4oo.1) s = \l;+ 2,

,/i il?

:lzsz . rV; =

406. 1) .',6 =&/i% > 960;

397, y = \lx.fpaoik

39S.

f,tbl

', 5. OYxxqir

s)'so.xa='vo+; el z{i = {u . slz = Jsa; t6 j,'o " = ilaq z ?r 4i/;

i6=16.ffi={Es; 6' irmt 'VBz ='dz' - tz 'Ja slz = ,[2. 5)

iH.

AKaaeMi'{Hnr piaenu

lilllliiliil:ii;i

i;r::::iiiitiliii: AIrEEPA Mep3reK A. f. ra

iH.

AKaAeMiqHni piaeru

lilr

gZS

412. 1)

r1ta =

110; rE

"E; i6

3y 98. i/2",2 +>

.liE

e,E

1[40 =

J,s

="PIn,

"!"

ooo, J-r.Vto;

' "t ='96t, r,/ie. V"E '{8. '{z - ffi,

='gEs

\E',f

a=!;+31

iG.

\ "Ji; 'tE; th zl i6; 'So; iE;

q1s-

g) i.F; {,E; .6r

i,[E' '.i[x' i,6. cr+. r) .,6; i4; i6; al

415-1\

i6; i[o;

960.

-lla;

u=4x

=!2

{$ffi ilii2:

a=\C4-z;

+1 y

{rl. foryâ&#x201A;ŹMocr Ao 417.

1 = 2o., 2 =

Bl,tBqeHHf, HoBolreMr,t

; 4 = 2'. 8 = 2s; 16 = 2a; 32 _

64 =

26.

I z , 1-=2". !=2". t 1 2.. L=z-. 248163264 ".. 418. 1) (-8F ( 1)r'= 64 1= 63;

416. 1) y=-Vir;

4lci;

slt

gr s''

?l' =s. a =!. 9l al I

1=!, -a'=!3412

4t 2" +6"

r = 9 * 2 =11, =1* a36727272

srlll +t-2.:f s' i2 I 25'=8,5+t-0,04 t7/

4,46;

6)9.0,1 '=9.10=90.

326 iiti A'TEEPA

Mep3reK A. r' ra iH.

AKaAeMi'{Hnr pieenr

:iii,:}illili:lil

::iiti::illtill:

AITEEPA Mep3nrK A. r. ra iH. AKaaeMi,{rinn pieens

419, l) a1 ar atll 2\ tt1 : a5 = a': 3) (a15 = o$'

425.1t

. taJ)d . dl di3 . o4 tlt ---.-iE = -;-=oI

4r -5 0.01

5\ {r5 a3=azl

a' ato otr - a 1: 7\a-ttat5=aI' 8\ ar' a'o i ae = a12-2ite - a'

o,' n.r,o

9) (d 5)a = a 'zo; 10) (a,) a (a,), :

(a-313

42O, 1) 2s. 2 1', 2 " = 2

2t..r.111 ' t3i

= e

a3. a6.

\',+"

a-24

426. r) 8:

=21=i.l

;;r",l-fr,"

sr{

z1 au

4)106= +--l

lr ';:

3l b -

a oi Gi: A1

t3, =

Jlsi

x " lx6;

(a.

- 2bli

= 4t"

az+-

t1 Jz

4) Vbo'

328

=2it =

J2" = 2l

= ^t, v3

39tr.

":l

= t0;

+-);

3 >O,

(-*; -1) u

'>3;

(?; +-), 60

x' 6a 7>0.

Vc:

x', ,(y) = (0; +-), 60 r > 0; 2\ y = a3,, s = ai, ,(y) = [o; +-), 60, > 0; ',-Dlll 3) !=lx+11 "rC tl: r-).60r-r.0,.r.-1r

424.1\

V6u =

e) ,1[s

6'; 4e'r;

3) \ns =n

(5a'); 56d6: 5) i/r t y tx - stt:

!tl: AflTEEPA Mep3neK A. r. ra

= t6, ,(y)

t La, D(g') = (0: +*\1 k - 3)L6, D(s) = [3; +-),60 jr

8l Vr- b' = {d - b )s. =

loo

6t ob' alb'l

3t ro' .c' =

2) ta" =oi; , 5) ,12'" =2"1

-{a"

y v= u=

4) a=@'z-6,-71,, r(y)

6 -es1i = 1y 3y1a={1r

=,143 =23 =Al

3 243 lnTl"=li?91"="/tP'-l3l' \ 64) \64,] \/ 64" \2/ 2" 32 .ts. 32

427.|t

429-

Ed ro ^r

=(#,)'

"a i .lloool' J/10" 19 \ r25 ,r 'J 5' 5'

zt'1" .

x 4) V3o (3d)'; tt llto - tt . t" ot",

a2s.D yli .

t l'=Jt =1 ", "r".=[\32) \32 2

sr o.rz;

b, BnrLno' 3m,n, =3{n'n": -

'={#=;,

',l':J

=4,

=Ja':

b) t..b)

v10'

ooo ooo = -sooo,

tt 1 \4)

t6.

6. 8r3HaqeHHr ra E acru8ocri creneHt 3 paqioHatbHl,lM noKa3HtlKoM

/1\;

33 16 226.23 2" tl' 23 2' -to--"=2

421. 1) 53 = trE

s.Jroo'--s

i = ,/]!gq = ro = 1= r?. 1216 6 3 3

3) o,oo81 o'5=(o,oo81)ii

36=3':;:

5.r00

2) 10 000' = l/10' = r0r

, ?, r,3,'1" t)['oJ llr] I'ltl'zs,'rl25r' t27)-% 27'

422.

7) 27, =:127 = t127' 27 =27 3=8rl

9 125" 9 9.9! - ^,, ^,. -;ii5" 5r:J-

^. u,

I = 5.'\ 100,/

^^^.i^r 31364'-3'=":

l2b':

a3+6+21= a22.

t,4)=2"=L, 4t9t.27,=33

rr r

2t25'

4 =J4=2t

'i6F

iH. AKaaeMi,{Hnr

,!u

o,ai.

piaexu :illi:il:lill:i:i:l

+ 1)it

v=@'! x 30)6, t(y) =(--; tt! I) a' d.3 =a6;

-51

u[6; +*),60r'?-t 30>0. / '\J \a,J ob;

: t: : 3) d, ta3.-a? , -a6l

4' ao6 . a\5 = aa,.

rr (,"/

tloi

6) \a a' =at a'=an

7\ ai i |la, = az : a6 = a1r.

8) (a '.1\4 =

a1.',

??1

7O\

at.aE.a3 =aa'aa =ai.

d"o" 1.. Lzt _l_4

illl:lfi!*illl

- ';r

^i.

11) (ao,)o

/ r !\i

13t \a6 b,1J

UTESPA MepstqK A. r. ra

1 -! l,'a ill iaa =a3 = a3.

r ! =a, b'.

iH. AKaAeMi,{Hr.rn piaeHu

llt:

3Zg

..'-6,' . ... t20,,,zi ,zo.t' bt 12") 1.4' -l;l l;j =l.:r.J 4,

.; ;'i: = "' "2 "; lot \otl . lo 6/ =,' ,'". t4\ o: . o''" .

43O.1) b3r

t,t: =6"s =6i; f ?\" ! 5) = D',: l6',l

7) lrE tb

=b.'6 =bE =bi'

g)o b, o 10r al o''

= a'

o"i6-

16 .

bt'i

i .bi

=bo -1; 111 i b,b1=b 1=b4.

bt.,lb=b,'t=bI.

a .: :,: '-.'_=o'"'=Di bt

2') b

8) (6r3)a.2160,-606.(64f,=6i,G 433. a >

16) (b1){r : (b

o,a) 5

.b1 = D '3

=a)b'zi

(bo.3f.{ =

b43

431.1) a\" srd 3r3=J, =s;

ll\ 491I "

I J r,2" =t1,2t0 .1,20' t,2r

\ bJ

=,2 "t

b03'

bi.o4.

2t 2' . 6"

60'3 . 61':

r\16

7' =B4B:

"/ .16"' .\2") z,

432. 1) 53.' .5 r'3 .5 ': 6 2) (7'orrl t7 B)

/ afJ

le?J

lr'1161 l |l

33o

i:::::

/ a\, =

\s,/

! t3

'z.6

2a.4.2,.4 2, - 5n -

,1r (Va

O,2.

," = ('"-/

b15 = (b t)3i

o ,i

+sz. r'

( lars: I

(6'i,)

r), ,"

*'=(-:)'

v = (,3)',

4',)

a: = la"/

;

^,1

2) t0"'''40i.5- .lot ]oi 2r S, l0: 2? b = I00r t0; 31 0,0016 4 0,04 ^-0,216 J t0.2', i-fi0.21)-, {{0,6)') ,-

Il -t*25 tzs s*27.-tzz1, o,2'-o,2' +o.o' {\.125) I I I 4) 625135 25\5 \253 =(5{) { (5'9t5 (53)t=5'

53 .

5' = 5 3 . 53 = 50 = 1. I

z' .8-'

! l"

"'l;l;l l,T,*1.] L,I;l 3',,,2" 2-3,

t/tc =z: iH.

;

\r, , "f =7, 7 .

f-ll'l t49.r

ll 11 r: r, | 8r'.8" | .l 2' .27"

AIrEEPA Mep3rrK A- r. ra

)

t' |513i, | --t"? ^"-s' 2,.2'-zs.s:zse-2^ll: 32 256 frr; z;.J '

= s: = 81;

=rreri

ar (Jo)";

.. 32"1.4o- e'f \ 2t1 2t,.2t4 Zb 'r 640'.t64?" (2')q(2")"." 2L6 |=2h-z ^, t2 3' 7d 3 .2.3 7s ^ -6) r'"

= 6': = 36;

'16

ar = ta.l

'i.3c

,,e:=i="ii=r, 3601

l<,li)'

2')

1) ,6 = (b':)3;

i 1l-,ro1i.,roo,j l'o.rooll e,[ooo = ro: o'l'll.l .17 \r0/ l'7001 \7./ ) 8)

,1.

435. b > 0.

2) (503)6 54.s-5!,3 5n.3=50=1;

:; lzs"/ =\1./ =s' b) I

15) (' o3f

I) m =lm")'; r / r)' 5) a, = \rn,/ I

1'rt,t,!13 1A) b' .bt b1 =b, 3 a =b1,.

434. m > 0.

oi bt "\, J = arb 3l 12) \o "b, 14) (6o6f 5 bo.{=bo,3 bo,r-b01.

60,6

r) ('6)"

bj .b

r\ \oto.)

ba.

7) aD4.2t3 =2t'.21.3 =23 =A

"=ai 6-:

= djd

22.

33_":j-".

4,8f a,

'bL'=boli

.t4'=J2Lo

AKaaeMi'rHni piEeH" iallill:'::ji:.::

iit;lii::jlllill:

| . 2'3.3'n

,,:

@6.2')"

=L. 729

AITEEPA Mep3nrKA. r. ra iH. AKaaeMi,rHxt piBeHb

iali: 3gl

a3s.r)

I-;

0,04; .r,=(0,2),)r;

rx-2t)

3) (r'7

32:

-L lr"

2.r BiAnoqiAb: posB' trs: iB lle]{.ae.

499.1\ t

"'l,

a2 +

r\t

tI 1ij=1ooi l(.r-r)iJ =100 t; 3) (,.-b)t=0; ' 5-o;r=52r

2Ob 4h - 5b\ a - 5b r\ aa 12ab 4 1ab 1ab 2l m'-n+1 r' ,1 ,=tm.Dtm,_n+tt m' m+1 mtm lnt m' \mn ., ", tb,' _.J, - A(5, rlr) t' 7a' - a"b art1a bt ar =' b" _7ob" - be(b ra)- bs.

44o.

.:c 1= 0,00001; .t = 1,00001;

443.1, abt

m_r.

2o(a t3)(a

(p 5Xp+5) (p-5r(p+5\ p 5' y'-16+@+qv 2aQ+4) 2 u-8 1 1 ur8 -', 16-u" y-4 c \c 4)ty 4) a 4 -a06 - a') 16 a' t6+u'+8a-2a'-8a -16 -n\ s v'l -ytty - u't= urt6 g.'z 6. I g.':+6c-l 6c+2 --!J 442.tt(3c-t_3c-1.]. 2. -

(3c+1) _ ]:2 1).2c 3c - 1'

{3c l)t3.

(s,;)- (.:)'

("i)' 1t

= ,,:

- l)i

-/,

MepsreKA. r. ra

iH.

AKaaeMi,{Hri piaeHb

.i'

\+n;) tzn-,n; $n.)

(,r) _,

iLtiilillliiiii

16n J r 12

9'i

1,r,:.11,:l'=, _1,;_r,:. 4 \4 I 2 16

6Dq1 + 9

-6Do;' =

Dd;3

+ 9j

(.t/ -r'=.-rr

10)

/ ,\' / '\' \a'l +\a" I =a+a':

11)

o,-16o"-(r'-1s'"*25)=" ! !1 ? ! l b5 4brb3 + b3 + 4b6 . b34'] _ 4b6

12) 13)

-roda -ds - toa, -

- -2bi v ?

/. '\' , ,r), U"'l tb'/ .l("' a'l=1,' .6')\6' -a")=a" -2a3b'+bx, ,,) [; _J[; -";.,1)G -1)=("; _JG.J_,; _'. 14)

444, Ll

L'a\"

2) (nx'\'z -

-2oao4bo' +\aD1bo' (no i)'z

/ ,\' /

l"l

4\ m 3 5)

1)(3c +

332 iltiA'rEEPA

12c

(^i)'

9) (aq4)x +

3al

(3c

a(d

+ atb;

-a" -g _ la'+g) . 2a(a+s)(a-s) za@+a\@ 3)-2a(a'-9\' ato 2\ (a-4')(a-2\ a.4 4 "' x. 40 '4 a' 4 \a - 2t' \'-\"-2t--a'+2a-a'+2a-4a+8 8 = =-- G-8@tD la-zr"(a+41 2p" 2ptp-51 _ 5V_jL | _ 2p' o, 2p 5 "r,.5--p e'[t p" \p-s)\pns) (p+5,{p 5r {5 pl(s -pr 2j- :op -5p-25-2p1 5{p 5} _ 5 .

- 1,

6) a3 + 2a3b3 +b3.

2otot 3) (a 3)(a.3)

3.-lJ 6c-2

a(o

21 2a - aat +\at = 2dt A\ 2a + a\"bq" -6dasba3 -2a-saasbo3.

5a'-LBa+3a 9+12a-6a' ,

'l3c-l

(a lr(a + 1)

(6-s)' 6-g U 6f ^. o' u'-t2!t-36 ={6-116. y)- t6 gx6 lt 6-g te -, (5a+3i(a-3J+(6 6-3a 5a+3 6-ga 50+3 --- -. 441II a'.9

o(d '

a-1

2a'+6a

("L' -l' I-" r a'-t) x+a 'L (a a a2 + a + a2 + 1 . (" r)' = 9!l2g:))g_]I9) - @ + 1)' - t\ o' t

= A2l

4obt4b'? 4bz az) a'-4b" \.k-2bf t2b-a)t2b-at) a'z . ab'z 1 1 -2o = _ 2b + a - (2b - a\ . -(2b - a)(2b + a\ : (2b-a)"(2b+al -:-=l--2a 2b-d = a 2b' l2b - at 2a o o"t1l.o' a lota rl)-ora-1) a'-t ta-tf o,r --d -i-71

=-t.xea.

27t @ ti)ri = 27t, ,a

rlzal1

2l ta

x=125:

(,, ,,i)1 ,r., .x 2=4i x=6:

2.rr] ,,

Li =

.tto,ztf, I -0.008: l1l \ I,/

-(sa

4ban =

l'aas -tTao4boz -4bo1.

=n-n'

,l,\'z =a" -2sb';

2m'12 + 4i

!? 3

-2bcb

+b t = bx -23 +b

! B

ttti:{iii:::::iil AITEEPA Mep3rqKA. r. ra

iH.

AKaaeMiqHri piBeHl tl:l

333

('i)' * r' = *i * r, T v3 av\r . aon +rca + gy'z = g3

8a'+16g+8a'=uz +16y;

I I 1 ! 1ll 1 I I a1 8) c3 +6cscc +9a5 9cr2c1 6cec4 =ca +6c6 +ga3 gct -6cc =ca1

s' {,,)' ,'J{,, - r)= {"1 r)i,; ,J=,1 -,, ,, ((":)'.(,:)')(,; Dt)=(,i .bi)(":-bl=. \0,)

qqs. rt

oon. rt (oi)" *

-1,, -r'")1,

')l

=l"i ,2)("i,bi) , (-r)' [;)' =(-:-":X-i."]) ,) (,ii_(,ll=(,: al)(,i.B;). ,) (,:)' (,,1f =(,: -,i)(,t.yi,), +ao. rr

(8s".* )" =

(2'o.,

3ao35\era

ouo.

3v4

35).

u')

o u-"= (ui)' ("i)' ur ro,'"'y,(u,i)'

(u; =

334

"?bx

1z"1iu

_il=".1.. '/,

=ri(ri

rl,

"l(,1.f.

_6)

ol),

co.5).

;;-,1 1)=,:r;(":b; 121i

= 2i;

2iu =

_1)

2i("i

J = ri(r-'

\ 'l ' -i'=o,r tl

-rl-, ",'i

-,)'

I \ r\/ r r\ r _ ldr - brlldr + b,l= at b1 _-iT; Dt ,l/r r\ aibi a,b,\o, + b1)

r11.

,o\,),

\ze za' ) o,')"-l';"\I "

(.;)'

:i;:::::::::;:::::::::::::::

iillijilliiili;

a+l

a'(o + 1)

^. a"la.+c'l .l (ai n .r/

,,1:"1

.b;).

::ii: AnrEEPA Mep3nqK A. f. ra iH. AKaaeMi,{Hhfi piBeHb

all

u)'

\a' - r/

=(n'",' uri)(n"'*-u,i)

[;)'.(,;)' =(,i.bi)("!

4) c. _ci =ci\cr

^;,;(^*^:,:,,).

+sr. rr

-";)(u;."1).

[;)'.r. =[; *a)(o aoi *s), ,"",'-(r'J' 1"" ,i)1"" -2:""' ,:) l"i,z"ll"i-rl''

b?),

-r, l) ,i(,

,loJ.("'

ttt

\b,I 4b'=b,\b,

e'1zi .ai -31

zt = z,'/ \zt

oi(,

"r:)

,) (.,:)'.(b;i =(.;.ri)(,;,:u;.,;), ,., (,'*)'. (r':)' = (,.' * r*')(o; o':r;*r;),

5.)

"ib:("l 6

,3(,i

/,\'

r),

,y ,03(ro3 * J.

oor.,, (,i)' r(,1)' =("i *r:X":,:u:.o;),

\ 1/;

4) bq3(3ro; -

(-;)"_[:)' =(-:,;)(-;.";). r, (,',)'-(,' 1,,1 , -;1. ,11 ,"1{-l

,) ,l ("" I .6)=,;(.1

L:) lb)' l"; bll': -b')

{,,)'-{rl)'=(-i

tl , lm" '?i

(":)" _(,:)'

6) (2'L,\, -

,:b: _.,i0;

o lo',i

ro|=,i Ll

=r":

"0,",

\at

\0,

+ 2b. )

+*)

]

at - zbi.

\oi + atl 8)

L,l h" .')(, ,'".' .) ^.^.;-, a,nresPA Mep3reKA.

r..

iH.

AKaaeMieHrfi piaexu

i:ilr

ggs

tl5

t r i t t\u i,.tr+Fa.3, IL - - - \ 5,+3. I

'o''l).1-ul=1, rt [x, 6J .r; ,l ' \ r ?/.

/1 ld'

1',la'

2i.Ei

_25

\s.

_rl

tli

,\t6

-,e'I - (rl)'(rll' = B" .8, . zb s

1s' +e"J

22si

)

r r r/, rr,d z.lJ s,.2,\24_3;ll s".z la, zt ", , , -r- = , ,, | 3' 2'=2'1 8=216.

rt,'

I lz,"g.l I t-, [2;-e.]

1t' \ +sz.ye!!!:-!.=ol. 1"1

,, I r' ,r'lr"

= JLi ,_ a,\o, $l \,; _t)\,, _z) ,,_t 2l _ ^ a' rt -,,-, _ 'ir)= 3. --__: r2r:-:- oi 6i(5; = 3r.

r : r r ltu l31 2t-8, -, -, 24 =225+216=441i lI '\ 24 -3, )

o"n.,, tlr

. r)

-ao'rra"5

(au' - r"")

)

aq') _ (ao5 bo5Xd+dorbo5+b)

(ao5

btr5Xaor+Do5)

a + 2ao.5bo.5

., (ao5

5), + (ao. + b" "1.

+b-a_ao.,bo.r _b

. b*

------;t' e

:2!::!:t!r ! :4i!:

ao'5 +

bo;

;

2a + 2b

- 2(a+b).

a b'

/ , \/ '

.1, _ir;) j =b'" _1.1 b,:"

-_tllai*tl t,ti il 2\ .r lr, \"' - ul ',\",-a")

o',)\"-'lu,-o)G',-oi)\' '',u;

'r t"\a, 'fr= a6b;\o' -brl -t')

aro.t

_to.|r

a'(a t)i.",',

" ,"(.:, E) I \n" r .31 r 8i '1"

,,;(.t =

36) r

- 6i

r L

-l

-(S)

ll ! \ I 8. 13. li 2. 84 rl 3),

ou".,. n I l.2, tt ' l '-- - ll.' ) ,r u:

_,,

6i m'\m" { : +oii "l

a. 4ss.

(rvr)

=1r'fi *1"''"ri ,?

ll=

(,1

,ii ri, o,b'\or brJ.b"

.blX,:-ri

@-ar!

"',0'",

tt - liui)' = a" + 2ab + b"

u\=(,,,

":rl)(,"

ab = a2 + ab + b'

r,,,1r1)

\^r ,i) 1,

- na - ms +

min - ni -- 2n.nit

,\/

,,,, (,,'")',tz o':ltz.'_o"t 1

r;) e')"^ l2i) " =r.o. -r'=z' z', t t \/ \ / ,\': :r lzl-z')lz' -z )=\2,) e't' 2 -r'=i-i=i' r. ra iH. AKaaeMilHr4t piBe*"

mini .

=zi ' z-"

u n",, lr

336 {liAIrEEPA MepsreKA.

a'to -

)\a" ' ai)

orl, -,'.!', - u)1" -

tn'16 6/

: 84 ^. 31 .2t _ 21 (

6)(,,;

11/ I a"

"' T;l o

,,/

-a'lla,

la'

,, ("t ,r) " iiiiiitiii:$il:!

\' 'i)

o1",2-o',=s,

l,:b;::l=!:-4),; _"bl I

-"('l-bl)";

,1r(;^_",)

ii:litlitil:jl:t A'TEEPA Mep3reKA.

,(rl

--" _,1) b'

r. ra iH. AKaaeMieHnt piBeHb

t:!li

337

{ .1,^ ,, ",1(t'-",:) (.'-t)(,,i .r) r ^i+t-t ^L ''.

^;Gi) *(,,- ,)= .l^: )

4) Cnpoqycxro,liBy qacrrHv ro, ol+rHocri:

456. ltCrporqy€Mo iiBy qacri") roroxHocfl:

(

,?+,)l?l ^"."' i-'=n'm': \m, +mn, mt+nr) m'+n' ,

m\n'

I :\ - n\n' - m'1 m

-l

r' a ao t

(a05 +-t),(aoi

' - 2 - la + ao ' ,oo' - t)':(do6 - l)

2ao

" _a

338

2rx -

pi6no"i6o.

o-ttGtoii tt)

+ bl

2b'z .

"/L a 1o 4 t 46 t)

zr' , yr ''.i. + 2s) :,iai(x y) z(r + 0

-r 3

(":

a,bt r-

(,-r

asba b3

L\/

' '\ brl\ar+a3b3+b3l

3y6

11 1 -3tiv6 +3y3

t t _ _ o.b. | |- I 1 b'_a" a,.bB

1,.. +

y.J(,.

t"oi) (,; - ,;)'(": ., ,:)' ,(,1

3!.J

t, -: ,i -ai

tsa. t,'n4ng PrA.r=!1=?9=!,

t, ,,"r = 19 = ?, 459 Bidnoaidt: !: 0: ?: 99 iH. AKaAeMiqHur piBeHb ir:iili:::iti;:l:..::l

,:)'(;.,;)

2- I t ,(,1.r,;)(,;-,;) +r\'/ r\/ r l*. - ,.J

_ ?t-

_ t3 + x6g6 +3r6a6 +3a' + rz - t8gi

AoseaeHo.

AI|EEPA MepsncKA. f. ra

i-----i = /

t 2xiy'+a+r+2x'a'+a t,t t r\/, ,\ x,y1\x, + s,l\x, a,l

lt r\'/r LlLj! !\ l-" v1 la6 -,6Jla6+/6, v ..;l ! t ! tt I I 11

oit;

|,,\t"7tL la'+b'l\a3-o'b"tb,l t t tr/ I I ! tl , axbitbtl\ortb,l \a"_t"l\o3

il:::

2@-.'G1 -bi)

b,J

2bz. 2a' _2b' = 2a' -

,t- + ---:-=---Yr ,/ r rl ,'u,\,, _c I r's \,(, .v,1

^. . irt + 3y"

oi+bi I ad b3) o3tarb'tb1

_tl3b3= _.arb3

2b,(a _

- a-b

btla

,,t

BiAnosi}b:

tttl _

2a'

b,) _

-1) a-1'

t\l

n \

+ b)

x;y;1r.- s) (2t

(ao' +1Xa0.5

2ao'

- t)'

2a, (a _

2lt + D\ I1

3) CnpoqycMo riBy qacrxEy roror{Hocri:

oii t tl

t\/

457. lr' I.

-o5 ol a I l;d',r-d ool z

(aq5+1),(aq5 -1).a05 22 . aoBeaeEo. =

blla t

1". "!ri t

aoBeaeHo.

(atr" + 1l(oq" - t) zaa" -(aa" +11

I oJtt., I "t-t

b t r

alb'

AoBeAelro.

a+au" -2-a+ ao" +2

t\,

2b,

z\"' *)\"+"1t'+r)

^:)

2) Cnpoury.vo iiBy qac.HHy roroxHocri:

bJ\a +

- r/r..

I ^a.s ' \".2""'n , ao" t2

2ab, +

- b- - a, - a,bi - a-b

o"b2

(0 m)

n'l

a'b, 2aJb 2ab2 |

!??lq:1 _2a, 2a,b

n" nt mn n(n =.F_,,)= ' J.i ,") .,-,,,=m ,G:-,)

,("i ="("i f^r(":.^t) t-lr=

a')

z"a +

\r \ / \/ ' ' \ a.' t,)\a - a:b, - bl \at' + t- l\a + a-t- ol

P(B' = Ol

10+20 30 PtDl=-=-=-. 45453

i::iiiti:iiiii::itl AITEEPA Mep3rqKA. r. ra

iH. AKaaeMi,{Hun piEeHb

Itli

339

45e. 1)

P(,4)=#=*;

Biilnnaidh:

214 15 lo

A4 30

PrB)=a=1. 30 10

3l P(C)=:=-.

46s.

m L 460. Hcxaii y tiopobui r.6innx KyrboK, y.horo (r - 25),ryn6ok. '''-PlAl n = x-25 rrro ra 'vMoeorc ralaqi c."r"r"t" ? 7 5js=50;r=10.

* --li z, Mscvo pisgrgns: =2, a-25 7

su;

fiepeBipra: .,lz

=2'i 2x 1'4t2x

5ix

2-5.

3) Jx-6 =-3: (V'-e) =t-3ti! BidnBidb: -237

D J%-

7=B

- xi s'

Jr-'2x' 2r.-l=1 2ti4r=2; "=j.

.lrt -1 = \z ; 5

o=o

nepeBipRa: 1/2

rpaBr.rn',8o.

Bi)noatla: L.

4).,8"-1=tlF*sr

1s;

2, 1=x'+4x

4 = a: x

= 12. 243i

IepeBipxa: x1=-bi G11 Bi0no6iAb:3.

237.

464, 1) V.r-3 !,12x-3; nepeBipra: {6 = d,

-2,+s=*; (1t'-r'-sl =li 's 2'+3=a3: 2r= BiAnosiAb: L5.

3;x=1,5.

$: 3=at ("[ r)'=n', '). 3=16;'-1e. flepeBip&a: .,its s =a; u/ie =n; a= I * "puu""u"o.

462-D

Bidnoaidb:6.

sr lz*fi'*z =a; (]z. G'.2 ) =s"; z +{V* =s; ",,F * =z; x'+r=a; xr=1:.x,-.1:r,.1. lepeBipnai t, = -t;,fi * trEi = s1 ..li + z = l; 3 = 3 - rpaBrlnr,Hor r? = 1i tllJ 3:i 3 - npaB,nbEo. \q. Bidnosidb: li l. 6) Vr'+rg =21!*1; f + 15 = 8(' + 1); + 15 = 8' + 8jx'-8r+7 = O; '\=1; " BiAno'iAb: \i

=J-11

ue uae

euicty;

nepeBipka:

l 6 l6 I "=l. I b i4 ; 5 {r ,, i-t

4 tlz" -zs =V5;+10; 12-25=2t+

BiAno7tAb:

-5t

10;

''-2x-35=0;

flepeBipriaf nr

= 2; J4=-2 -

aenpa.afl,Ho;

-G'

BiAnogidb: 1;

-1.

34o

+,,lVi = zt.

n[V

z; r' + 3 = 4t r'

lal: AITEEPA Mep3rrK A. r. ra iH. AKaAeMi.{Hrai

r,=l: u4=r, r=r

npaBunbgo

- 3) = 0; r, = o; a, = 3. - npaBl'rn6Ho.

sx + 2 = oi r'\ = It s, ',h; 2-,;3,-2=)r\x2 = 2. tr = 1;1= 1 npaBvnt']jo; x,=2a2=2 ', trpaBxJlbHo. BiAnosidb: li 2. q \Ex'z -Sx . 1O xi 2x" - 3x - 10 = jzi x2 3x 10 = 0; jr, 2t.x, - 5. HenpaBu,!6Ho: .r, = 5; r€peBipxa: t, = z; rETzt' -a C2t 10 = -2: 2 = -2 16=1 5=5 rpaBr",l'o. $.!'1.5 IlepeBipxa:

i6s

2,x2=L

z1 .lz+ t = x - 1: x + 1 = 12 - 2x + !; t' 3:. = O; x(r HerlpaBrrnbHo; x,=3;2=2 IlepeBipria: .r1 =0i 1= 1 BiAnosiAb: 3. EpaBx,,r,Ho:

x\= 5;x2=7.

1; x2 - 2x - 35 = o: ,\ = 6;x2=4 4\ \F-s6=J2r-1) "-36=2' ge uae auictvr r,= riepesip(a: = -5; rlEb-36=J-10-1; J-rr=J tr ', npaB}1r'1,,so. Jta "{l 7.BiA o6iAb:

BiAnosiAb:1,

/" 6{-9-,o=3; yfn-rs=a: a a x,=a: JB.9 a rb ai Jz? 3 rb 3:3 3 npaBlnbgo. Bianoeiaa: 9: s.

.fi=.'fi

BiAnoaidb. nopelliB HeMae.

D .'lSr' x 15=3t 3a' jr 15=9; ga'' r 24=OtD=289 i x'=3.

FcMA{iMicrv.

BiAnoaid6:19-

.--8.

fi* s=r6lxr,r,r s r'r:S*=O;x l.

r-2=Oixr=

rrEPrirPnd','.-''{"'-;_'"

.rc,

npeBr.L'rLgo.

2- t=t';x'+

x-3=2x 3t.r '6; .r=6.

a65.1\ J2-r=s

16ir'+ 2r-15 =0jr,=

tz= 3'

4\ {,"

x1=

= 4i

Bidro8tAb. HeMa€ IlopeHiB.

z,r-t=z; ,!4=z; z=2.

(i/t-4)" =23; r -

Bianoailo:

{i - z; 2, -

s\,Ex r=J;-.2x-1=x 3i2x x=-3+1;x= 2. rrepeBipKa: J, e>1= J 2 3t Ji = J- "e .ae sl'i"'y.

BianoeiAb:2-5.

2\ lx - a -2i Bidnosidb: \2.

Bi0no6iAh:10.

461.1) J2r.-l =21 \J2r-l)

\ \E;1

= 1: xt = r,

Bi0no6iAb:5.

piBer"

l{i{litiitial

:ilil:.:tilllilli AITEEPA Mep3ncKA. f. ra

iH.

AkaaeMiexr,rr pieelts

i:i:: glr

5)=(t + 2\'i 4x + 20= t2 + 4t + 4t

fi 2@i=x+2;4(r+

= -4; 2J4+5 = 4+2i 2= 2

IlepeBipKa:

Eerpairn6Bo t"=

6=6-rpaB[nbHo.

rt'2 =16;

t; z,ln+s =a+z;

BiqnoqiAb:4.

A1,!tS - Sr - t = x; J15 - er = x + t; 15

t, + 5r -

14 = Oi ta = -7; nepeBipxa: xl =-7; 1tl5 -

- 3'

(t + 1\'1; 15 - 3t = x' + 2t + 1l

r,= 2. 31-1 -1 =-7: 5=-7 -

HenpaBrnbHo:

BiAnoqiA6:3.

a 3x

"" =o; u6-g" "'=-t'+2): "=(-(x+2)r'i .r:+4,r +4i 2x'z+7x 4=01 D=81: ,,=-n, t"=i.

8 3r-r? IIepeBipKa:

|*r*fi

1=o',=o

-4; -4+2+ J8 + 12

16 =

O; O = 0

r, =

npaBunEno;

1).[0-3r =-r;

;

He'pa!&r6'o.

-3r=.r'; r'z+3r-10=0; h=-5x,=2. fiepeBipxa: rt = -5j Jto*fs=s; .85 = 5: s=5-npagurEHo:r,=2: G=-z; 10

2=-2-EenpaBrrnr,Ho.

BiAn%iob: -5. 21

x=Jr+5+r; r -1= 1G *; x' -

2r +

-1; -lJ-t+S+t; -t

nepeBiprca:

", 4=4-npaBsnbHo.

+ 5i t2

- 3r -

HenpasunbHoi.r" =

4 = 0;

-1'

4; {= J9-1;

BiAnoqiAh:4.

$ nEr\ .r, l,5i .r,

= Zt + 2',

+ 5t + 4=

4x'z

+ 8x + 4i 2r'I +

3t=U tzt

+ g)=O;

= -1,s:

2=2-npaBvrll,',o. BiAno6i0b:

Ez,zs-z,s*s =-3+2; 1=-1 -

EenpaBunbEo;

r,=

l) \,'+tO-rt=Zr; a,&l tO = Zr + tt; 9(r + 10) = 4r, + 44!+121t 9,r I90-4,rr t 44x t l21i 4,r/ - 35-r - 31 OiD.72gtr,. .t; r, - -4. '4 nepesipxa:

,[!l-,o \t 4 BiAnoqiAb:

342

::tt:

2oi

Henpa,

BiAnoqiAb: 5.

cyMa HeBiA'€M[r,rx q]rcen, .rjrcno HeBiA'€MEe, orrne, piBHfinHs He Ma€ Rop€niB.

,&J-Jf

-.r =5: oAs:

PiBHtHHt He M6. konaHiR

1x-4>o']*'x'4' Po3B '3KrB l

1t - t - o; l-

seMa€'

Vr-6, Je r l: o.[a: r- '-0' r- 6. j 0i fr>6' 16 -.r ljr < 6r Ilepesipxa: 1f,11uftl = 1 6 = 1 HerpaBurrr,no, or'{e, pis'rr'n, a)

=r, 26+Jx+1=zit .,&*r = -r.

He Mae

piBIIssHs ne Ma€ xopeHiB.

{; +zda' -3 = o; aai.{isa: {6 = r. t+2t'-3=0i2t'+t 3=oiD=25jr,= 1,5; ,, = 1. {6 = 1,5; .r=-s,3?5; Vi=L ; = r. rlepeaipxa:: = s,azs; iFg,g?5 +zifi a,gz5)' s=0;-1,5+4,s-3=0;0=0 rpaBanbno; r= l:4I+2a,Ei a=o; o=o-npaBnnEgo.

46a-D

BiAnMiAb: 3,375i 1.

zl G+iG-a=o. Ba:uisa: i6=r; r>o;,4=(G)'= t,i trri 6=0:t.= 3i !r=2. :3 I{e saroBonl'ns€ yMoBy t > 0. di=z; r=ta. nepeBip(a: +6 + ri/i6 6=o: 4+ 2 6= 0; 0= 0 - trpaBr{rbrro. BiAnuiAb:16.

2r-7J; 1b=0. BaMil,a: Ji =t, t>o; , = Qi)' =l; - 7t - I5 = 0i D = 189; f, = -1,5; r, = b. -1,5 H€ sa{oBonl,Hse yMoBy t > 0. Ji=s; '=zs. nepelip(a: 2 25 - 7nE5 - 15 = O: 0 = 0 rpasr{rEHo. BiAnosiAb:25. ql !; + el'G = t. 3ardsa: VI = r; t > o; l,[r = t": tr+3t 4=Ortt= +ra=1, -4 - Ee 3aAoBonr,Hs€ yMoBy t > 0. G=1:,=tIepegipka: {/i+aVr=l; I + 3= 4i 4= 4 - npaBunbgo. BiAno6iAb:1. 3)

5, * a

fi€peBipRa:

x, rox+25=Bt,-tla

,4,5- JA(-4,5\, -lr.(4,5)-20 = 5; -14,4 = nepeBipka: 't = -4,it llrnbuo; r2 = 5; 5 -v6.5' 11 5l[ npaBr{nLno. = b; 5 - b

s) .,60*"6*r

BiAnosiAb: 4.

466.

20t

G:r+1= 0; G-z = 1; 3a BlragaqenEsM apreMenrqEoro RopeFrs Jr 2 > 0, orxe. pisHsHs' Be Ma€ xopeHis. 2l Pli+t"lxt=-2, sa BraHaqeBH'M apr,abMenrqHoro RopeHs i6>o; {GJ>o;

zl , s;, s $,' ,-ai\x 3)!=2xt x-2t 'E't*-zt 2li12+7t 30 = 0; r, - -1o; r, = 3. ' ,z 6'-9=2zz+t IlepeBipxa: r, = -10; -10-J2(-10)'+(-10)-21 =3; -23=3setrpaBr{nbEo; 3 - Jr./' +3 -2r =3;3=3 rpaBr{n'Ho. '"=3i

=s; '-s=\6"-rri 2r','-!6;'-11a-20 4,8; x,= g. - 45 = Ot D = 362i \=

467. 1)

x,=2i2=2

BiAno6idb:2.

el "tz.',18

-l; Sv6-ll =-2: -2=-2 -

np"urronor r,

.91,

11=-?1, 222-11=-!1

zG-t b a-.

-1.

AIIEEPA Mep3nrx A. r. ra

2t,

V.r+1

iH.

A(aaeMi.rHrr pieexu !iliiiLi:!!:;:ji

i:iililrillt::l: AIrEEPA

Bauiea:

Jx+t .r,r.o.

Mep3rel( A. f. ra iH. AxaaeMiqHxt piBeHb

!i;l:

343

2t'z-bt 3 o. 2t, - 5t - 3 = 0i , = 49: t,.,= 5 !7 4 t

2t-5='i 1t 2 "-;

He sa,qoBonbBn€ yMoBy

1Ci =z; r+

9;,

tr=3;

;

= 8.

469.

,lV -t*s =t, t>o. "'-r+g*nf'-'+s=12.3aMiga: 4;t,=3. t,+t-12=O:tt -4 - se saaoBo"'1l,Hse vMoBy , > 0. x2=1. ,Q -a+S=S; r'-ir+I=o;.tr(t-1)=0; 't=ot 12t 12= 12 - npaB,lEHo:,rr = 1; nepesipRa: r, = 0: 0' 0 9-19'-0-g 1' - 1 + 9 + Ji' L + I = 12; 12 - 12 - rpaB'r6Eo. BtAno6i0b: Oi \. a=0. saMilra: {t--t; 7) lrF -+'*t 2:!S--s=o: :lA4 - z{;o)

t,-2t-3=Utt-3itz=-1. {x-z=s; x 2=zlix=zgi V.1--'2 = I r 2=-1it=1.

BiAnoBiAb: L: 29.

2; oI3: x * l. 3a-MiHar iF = i: I 0. 8t -1 - + -3 Vr-1 Vr+1 3 -2ti'?-ll I' 3 -'.- 0! t+1+3t-3-2t2 +2 - 1.1,3/ (i r)0,r) (, 1Xt + 1) r-l +--2.0: ir1 -2t2 + B! - I z, St = O, [r1zr s1 - O. it=0:r=1.5. ft-lxir1) L(l -Jt(r rl)/0i [i*Lr/ Ir Lltl:f*-1: x=5,062b. 0; *=0; {t=1,5; G=

x 5

344 tll

4sx

6 r-1 =(, -

49 0.

-48r '

r-l

-=0:

x+rixt

ArrEEpa Mep3ncKA. r. ra

iH.

He Ja,4oBonbHflc 16 .

."li

yMos! I >0; G=a;

1w+8=sdi; Vr'-gi6+8=o.

t,-9t+8=0;tt=ltt,=8. {[=L'=1; iG=s; r Bidno6idb:

512.

=t; t>o,

x=16

sardsa:

i,6=r;

stz.

g G - 4- = t: oA3: x 0. samisa: J:r i; t 0. ' 0i tr-t-2=O..tt lit,=2. : i-"=0: 1t -..1 - lre saaoBorElis€ yMoBy t > 0; '.lx = 2; x = 4 Bidno6idb:4. rt+5.-3{El;+2=o;

oA3:

>0; iu> -5.3aMiEa:

d"*s=t, t>o;

-4t 11.

(lrl)0r3) r;t,--z- lt 2.

=-z;

i6 o'F*z{6

-8t l.

j,,

=,:,

l--t.

iltlil:ilillli

t'z

+ 2t

BiAnoRidb:

=t.

{r+1,(t+3)

Ji=r.

8 = 0; oA3: 3

&6-= t, r>0. - 8= 0; t\- -4t tr= 2i 4

3 iu=64;.t=

<,6

i6=1; r=1.

garulga:

AxaaeMi.{Hrr piaexr

> 0. BaMiHa:

lt+t-2=o. [t, Irr. txr.rt*0, li,-t:i*-a:

o,A3,

BiAno6i0b:

BiAnoqiAb:

0; oA3:

/+l --L-rr-3

l{OpernB lreMa€;

-3

12 =

I: olIS: n r l, -r , 27. 3aMiHa: s, J- , , 2 Vx+1 Vx+3 I o, t-3-2J:Z--JLL 3r-t+3)-0.

{ 7r- 8' o; li-8r- 7=ottt lit,=7.

l0) 'gf -1{' ' l, Vr' t v*+t

i6=r.

12 Oitt-3t12=4.

BiAnoqiAb:

r-1'o: x- ( -, 5) u (1; +-). oaa: .F-*z.F==s; x-l !r-1 I.r+5 ---+-\--'-\,,--+ /;* 5 Gl r .-J-_-:_' saMirra: =ti t>0: . =-:

1L.

saMiHa:

t, 3t+2=Oit,=\t,=2. dG+S=L r+ 5=1ir=-4 dx+5=Z; z+ 5=16; .r=11.

x+5 -r+1 r-l

r) r \t

t'z. !

BiAnoqiAb: O| 5,0625.

Bianoeiaa:

(Vr + rl

BiAnosiAb:8.

J8+1

as.

('[ l)(it-1)

(V') -r Vr-1

"r-\' ,

; t=t-npasribHo.

BionosL1h:8.

5 Fl! =r, tt rLI li,r-l

) r

(16)'*r 16*r=a;(u'E)'-trQ*z. q-o, ({,J' -+E z=o. t,-t-2=o;tt=-1;t,=2. {x= 1tx I - Hc Ja,qoBo,rlHs. o,{3: Vi=2: x-8.

i > 0.

IlcoeBioKa:2v6*l -5- ,3

ixr ,,1,-8,. ''

{Vx I

> 0,

r < a. 1fi4-*y

lre sa,qoBonr,Hn€ vvosy

+2i6 "-s=0. t

-61.

r>0. z\ *'-t*a*nlV -r+q=6. SaMiHa: .,t; -t*t=t, t,+t-6=0; t1= -3i t2= 2; 3 He 3aAolonbEflc yvoBy I > O: G tt+ Z;,' -z+4=4i

i:iltiir:lilii:i

S-=2;

61.

r(r 1)-0;

AITEEPA Mep3rqKA. r. ra iH. AKaAeMi.rHhi pi8eHb

lt:l

345

0'-o+++.,6'-o+4 = 6; 6 = 6 f r+4+ J? -1+ 4 =6; 6 = 6 - rpaBsnbso. BiAnosiAb:0,1. IlepeBipEa:

*, I2.r-3 it" *3 - lL " VBr 2 E'*2

,.r.613. L2 2x 3 , e, " .|*, - J) "

E*z

--: i: .l-'' : \2x-3 = !3ir+2

SaviHar -1""

r-;

[i"+z t . ,r+z t 2x -3 a +2 -' l?!t? ,. 3x-__=0: ' ^. Vz* : - 2.r-B ^ 5.{ + 14 [5x +14 = O, 2x 3 l2r 3+0r

= 1;

3x+2-8x+12 2t-3

. -r.

-'1- 1.. -o 2"' - '' 10x + 11

r,1,

* r,r.

*, o,

.rEx - 3 = 1t .tEi = 1 +.Ex - 3; x + z = t + 21Ei4 + 2r - 3; D .l;i a, r = z1lzr4; 16-a'+a'=4(2r- 3)j.n' 8'+ 16-8r+ 12=0; t, I6t + 28 = 0. D = 744i \= l4i x,= 2. -r t HetrpaBrni"io: r^ 2r flepeBipxa: r, = 14; Jl4,z "Es-e =r: =r' 1= 1- rpaBr,n so. "lr*z-"84 Bidnosidb:2. 3) ./E + 3 - G + 1 = 1; uE" * s = t + + 1; zx + 3 = I + 2G+i + x + 1; "l; 2x -3-2-x=zJt l; r - l-2vGJ: "r- zir I 4(.r + 1): 2t - 3=O; rj =-lt )e,= 3. x2 + 2r + 1- 4r - 4= 0; t' I t trpaBxnhHoi nppeBipKa: r, = -li J2 r l)r3-J-lL=li !,= 3t 1= 1 - rpaBnnEgo. BiAnoqiAb: -11 3. i=y uE-'=t+rt xi aQ-',=1+2$ '+7-' 4\ 2.rE- 8-4x-8r.r 'h 2Jt x; -sx=2rt't:gx 4\7 x)tgx'z 4x 28.oi

99 '^=4=f

x!=-2;2'E+2- Ji +2=1; 4 3=1;1=1 - p=, ='; 2.f, -f, = t; -r = t

nep€Bipna:

t,=2i 3= 2 + 1;3 = 3 -

trpaBtnEEo.

- '{ = ar a : 6,9.

t,-9= t9;

"6=, BiAno6iAb: -2.

qzt.tl .,Ex+S=Z+nlit: s; zx+S=+++nEr S+s"-s; A-r=a"lTt s; 36 l2r + x, = 16Gt 5); ,'z 60x + 116 = 0; , = 3136; r1.= 58.. x,= 2. 346 !ii: AITEEPA Mep3reKA. r. ra iH. AKaAeMi'{Hnr piBetb li::iiii-::!itiiii:i

EII.E \/16 EI.

reDesio*a: 3i6noui6o

npaslnbao.

,{ 16

,=n

Ji-t+'t+1=r; "4-=1 ',Ei; t - x = 1- 2Jr + 1 + 1+ t; z,Gj = zt ri 4l r,r)=4.r, -4! 1.$t t,',=+, '" f

n.nFRinke:

.^ i E lf----i: vn r = v.r: .llL vlr +.11+:.1

-_ft;lt; 1" -,/r-*-t '.=-9,,/r' '2\2Y2

HenpdBr.,bH..

Bidnoqidb: He vae HopeHiB.

-E

al'Ea

tO,G + g =

11- -3t

s = s; nEa'at = t

rr + 15;

Jx. +

a7g.\ Ja-r.+'E+5=4 J4-;=3

- 4r = 25 toJr

5= 5

+ 2r

npaBllr6no;

J:r+s: a-r=s

+.r

+ a;

*n4+s =a;

Bidn%idb: 5: 4.

Jl,+s+J-s+s =3; g=B

3= 3

= 1;

6Jr+5+t+5;

a+'+"; onGls =ro+zx; s',lrTs=r+x; =u 25 + l0,. + x't 91t + 45=25 +loa+ x.', t'+ x

9(.t + 5) = 1'1- -5; t2= 4. repeBipKa: x,= s; n

]d2= 1.

= :;.,4s+rz+J s+l=5; trpaBnnbgo. r=r u6+G=s; BiAnoqiAb: 3i l.

Zuli + Z = x + a; 4(ir + 3) = r': + 6r + I :

fiepeBipxa:.,c,

6J,+5 ,ro"uor""ol

8. '

zt Jxi t.!' t + fit=a.Jx t: ., 7 - 16 - 818-1 +.:c 8.lT- = 22t 4J'l = 11; 16(t - 1) = 121; rcx=taz:'=#.

It=2.s. + L5. Ir-=ui

BiAnosiob:6.

HetrpaBrnbEo;

+zz.\ =3; uE s -s-u4o-ii x 5=s ou4o-,r+ro-x; 'li-s +lEoi x l2 :vrio-r: r'- 24x | 144 gllo 'xli 2v.24 x; -6',Eo !'z tsx | 54 =0:r-=6:r, 9. rrepeBipria:;r, = o; ',/i+ ]a =s; 3 = 3 - rpaBnnbgo; "[ BiAnoqiAb:

-1,Li 2.8.

= 1024: tt

58;11= 15

2\ ..8 +1- .,rGi=2; .,,6r*r=z*uG*r; 3r + 1 = 4 + 4.,611 + r + 1; 2x-4=4Jii; x 2=2Jx+1; r.'-4x+4=4(r+ 1); r'-8t=0; jrt,r .8r = 0:./, 0i xr 8. fiepeBipxa: x,-O;."E ."E = 2; O=Z o"r,put"n""o; x"=8;.lE-.tE-21 2=2-rpaBrnbno.

-=ui 47o.| J22-x-.110 t=2: .tE -=2+.t!o "i 22-x=4+4J10 r+10-';i 8=4J1o-; ,Eo '=z; to-r=4;x=6. repeBipxa: Jzz s JLf4 - z; 4 - 2 = 2;2 = 2.

flepeBipria: xr = Bi0no6iAb: 2.

BiAnoqiAb:

121+8-2t+3 2x-3

t_= \'l2x 3 2

o,u'

t' _!1L2 _ 6, f' u -z=o. o_n. t tt 5. 2 r Lt+o;

BiAnoqiAb:

rpaBlrnr,Eo;

20=O;

npaBlr,'lLHo;

,', = 4;

npaBrrnEHo.

4 "6x+t+.,Fi=a; Jr"+t=e -.!2 7;5t+1=36-12Jl t+7 r; :i:::t:iliiiltil: AITEEPA MepsrtK A. r. ra iH. AKa,qeMiqHran pieexr il:l gaz

- 6r; 2.Ji- = 7 - xt 4(7 - x, = 4s - 14x + x'zi 28 4r = 4s t4x + i; Ot x, 3i xr" 7. flepeBipKa:,, = e; G 3 + 1 + J7-3 = 6; 4 + 2 = 6; 6 = 6 npaBr.rrlro; x,= ?; uEtz +t+"lil =a;6= 6 - rpaBrnb*o. 12\li - x = 42

)t'z lox t 2l

BiArcsiqb: 3i 7.

s; .Dr+s=a Jx+5: 2' + 3 = g - 6$ + 5 + (.t + 5); 6J;+5 =g+ x +5-2r g; o'6+s = rr 4 36(r + 5\= 121- 22x + r' 36x + 180 = 121 - 22, + x,t t, - 58x 59 = O; \= \ r,= 59. 3:3 3 - npaBllnbHoi.r, = 59: Ilepesipka: x,. t:Jztz Jl5 rs*g *"69*b =3; 11 + 8=3; 19 -s - HetrpaB'nb'o. "E BiAnoBiAb: al J*+s+&+5

-1.

474.1\ x'-5x+16-auF -sr*m =o. 3a*i,.a: lEililili x' -5r+ 20= t', 1' 5x + 16 = 4= t'i t' 6r + 16= t' t' - 4 - 3t = O; t' - 3t - 4 = Ot t\ = -1, tz= 4. -1 -

D: ll

Tlep€Bip(a: x1=

f -5t+20=16i1.' 5t+4=0; ,1=lr,-4. s.'[' 5.1*20=o; 12 12=0;0=0-npaBrnBzo+zo =o; 12 12=o; 0=0 npaBnnr,Ho.

IlepeBipxa: rr = 1; 1'? 5.1+16 IIo; r, = 4; 16 - 20 + 16 3.,[e BidnosiAb: li 4.

r.t>0.x" 2-t'l x'=(+2 0.3a,Mil,a: ,Tz - 5t + 6 = o; t\= 3; t2= 2, uF -z =a; x,,2=s.f =11; r,, =sfi; .["" -Z =z; a' 2=4; a"=6; y,,=1uQ. tlepeBipKa: r" J6l 6t4 516 2 0i0 0: -r" uto, o=0, r.=-"fi, tt-4-5v[t-2=0:0=0: r,=Jtt, tt,4 bJt r 2 0i 0 0. Bianoeiaa: rll:l:r !18. rr 'f,'-r'* s * r'= 3a171 1t'- 3*-5 -.r -3.!.5 -12 = 0.. Bu*i.'u, G' -a"+r = r, t> o. 4!'zta

t, + 2 + 4

t2t t

5lx'1

-1; VG1)'!31-1)

-l: 4. at .,.6rrsrJ6=r2+8, BiAnoaiAb:

tr2.

Ba*i"a:

..6'iliilE

flepeBip&ai

r,=

.FCI"

34s lilj ATTEEPA Mep3ncK

g( 2>26=12+3(

a. r. ra

iH. AKaaeMiqHefi

r"= l:

rpa8]rrlbrro.

tz: 'rlx" t'dV 7r. tttii -'d'' -tz=o. =l, t>0. t, + t -'72 = 0. t, = 9j t,= 8. I ne sa{oBo,lEsse yMosy t > 0; 'V7 = 8; x3 = (23)10. x=21o=1024, repeBip,.a: J:r,ztVttou * tEozE,ltou = tzt or J*,f, .

tliT

2t=-t,+15;t!+2t

npaB'n6so;

r, r>0;

2) \ 2l;2=2

rpaBfrlLlro;

il z'{'" z,,n.4+3,r-r.: 2"8 3, lt" (r' srrll)'15. B"*i*u, .,frllllli - r, r>0.

npalgnbgo.

1t'z-9t-26=t'' 3r' 9t 36+10=t?;3(ir' 3t-12)=t' 10' t" to fi' lor " 33 3t + t'z - 10 = 0; t'z + 3t -10 = 0; tt = -5, t2= 2. -5 - He 3aaoBonr,Hs€ yMoBv , > 0. nEt'-s*-,6=z; 3x,-g,.-26=4i3x, - 9r-30=0; r,-3Jc 10=0; r.,=

-4t 5= 5

x'-4x sn7 tuzo*to=o. sultri'u, 3!F - 4* + 20 = t, t>0. 2;t,=5' 2 - He sa,qoBonbH.se yMoBy t >0; t'-3t-10=0;tj= x2 4x+20 =5i t' 4x+20=25;x2-4x-5=O.1't=-2t x2=5, IlepeBipnai rr = 1; 0=0 - rpaBrnbHo; t:=5; 25 4.5 3,85 4.5 + 20 + 10 = 0; 0 = 0 - rpa3nnr,Ho. Bi?nosi1b: \t 5.

+(-1f =3 (-1)+?j 4=4

x"= 4, J4' -3x+5+4'z=3.4+?; 19=19

.hc

Sauina: rVr3

nepeBipxa:

475,1)

, n.t - a.t 1. ne 3a,qoBonbnse yMoBy t > 0;

z;', - zx - 4 = o; \= 'rt,',=

,lrt

BiAnoqiAb: 1024.

5t = ot t,

.{," -e," G -

-t2 + 4J22 -s -

t, I > 0;

se 3a.qoBonbFs€ yMoBy t > 0.

Jx" -S,+ZO=4i

o r zo =12+3.5 5'i 2=2 - npanmrso. ",=rr.,8.r' BiAnosiAb: 2i 5. 2,"+a,-zJV+st z =5. on3:''z+3, 3>o; J4,ur.-,. saMiBa: uG.+3.r-s=r. r:0: " .E i ".1--; --3- 22 x'!t :.J 3 t;2x 6x 6.2t";2x'? 6x=21 - 6:2i'z-6-Bi-5=0; i 2t2 3t+1=0:r=1: t, ==i tr=71 l; x'':x : I;4x' l2r lJ=0; '['",z, a 24

15=0i rr = 5;t,=3.

He sa,qoBon;sse yMoBy

t > 0.

uF-ar*rr=a; f - 3, + 11 =g;.r': 3jr+2=0; \- 1; x,= 2. repeBip(a: ', = 1; 2.,[' - a r * r r = 4 + 3 1 1'; 6 = 6 - rpaBrrbHo; zuF-a.z+n=++2 2 2';6=6 npsur6ro. BiA o6iAb: \ 2. 4 Jr""-6'+40=,'z-3'+8. SsMiEa: J2x" 4, + 40 - t, t>o; t: 2r2, 6x + 40 = t,i z" ax + a + n = | ; - s" * e = | - tz, t = - n, 222"" 2t = t' 24: t' 2t 24 = O: tt= -4i t2= 6i -4 ne sa,qoBon6lrse f >O:.lir'-Ar*+O =A; 2x: 6x+40=36; x'? 3x+2=0; .

x1= 1; 12= 2. 2;

trpaBur,so;

piBerr l:jaltitliltllil

r, = 1; J2 1'-6.1+40=1'z-3 1+8;6=6 Jr.2" . 6.2+40 =2" -8.2+8i 6=c trpaBrr'Eo.

IlepeBipRa:

npaBvrt'Eot x2=2i

Biano6i0b: 1i 2.

:tiliiltliiiiai

AITEEPA Mep3ncK A. r. ra iH. AKaaeMi.rH!.ln piBeHb

itair 349

t\ tt' * tO, + .[r' * z" - tS = 123. Sal,liEa: '[V +zt ts = t, t>Oi f 2x-15=t''zi 123 =0; 5t'?+ t 48 = 0i 1Ot = 5t2 + 75i5t'+75 +, tc, + 2r=t2 + 15i 3,2. D = 961.. tt= 3t t,='x'z+ -3,2 ne 3aAoBonBns€ I > 0. + 2r - 24=O; at = -6t x,= 4 x'z+ 2r- 75=g; J"+Zr-U=S; nepeBipKa:.r. 6i5 r-6)^+10 l€) "t.//(-6,*11 6)-t5=123:123=123 nparpaBlrnbgo. rrvnblo; x.2= 4t 5.4'+10 4+ J4' +2 4-75=123; nA=f23 Bidno6idb: -61 4.

Ir'+t-sruor<1. lr 1, rxqo x:1:

476. 'f(r\ =

l(') l(r) 477.

3pocrae tra rpoMi4i1!&x

hx + b - 3aranBEr.Ii Blrrnsa, 2h+b=b, l2b=2. lb=1-

at'

MaeMo clrcreMyi

foa-:a+r= 2. 1" =

{a ls I

1)(r + 4) = 36; + 3r - 40= 0;

,l2x

Il.

9a+3b+c=10:

o.'2| .

4+3b-2=1Ol

Oll3i

l2t 7-oIlr 4'or x-4-

=o. [, 2 JiT-ts,rn=o. Jr' -, lzx -t z ot , 2=.1E"'15.+28, x2 4x+ 4-2r2-15t+28i*

x-2 Ja

4x2x

11r+24=O;

x,= 3; 2r18. BiAnoeiAb:

t'93 lr=9,

r'z

r-t 4) ." - -Jr-4: Jzt 7

9a+3b+c=10;

lr=,

=0;

2r-3:O. +3 'lx- 2 3r OA3: i.x z" -Ol x. O. 1@r+ sXt a=z; (2, + a\Q 2\=gi2''2 4x+3'-6-9=0ibe' r l5=o; D = 121, t,- 3t t,= 2,5. 2t

Bidnoeiat

9a-2=2,

18a+2c=2,

lgd+3r+r=10:

4" D=-a'+

o; (r

aaranr,Elri BLrrnnA, Ma€Mo clrcreMy:

',= Bi6no6iAb:5.

4 s,

r.I0: r .rl oA3: fr>0i lxa! JrQ+q=x; r(1 - tt=

:; lz**a= a: lr=-2.

+ bx +

t11" + a; =

+ 3x - 4 \= -8;

3) J). J1

11.

BiAnoqi1b:V=-2r+1, 478,

u(r x'z

Bidno6idb:3.

( -; 0l ra [1; +-);

craAae Ha rpoMiniRy [0;

lzr+a=

l-9'"r. r.r r.G-4=6; oI3, {'[.r-4-:0:

4so.rr

fr-s>0- #;t ). 9. oA3: I 5) Jr 9 r./r= .h-9 lr>ui e^ j--G-n, * ..9--6-"-9: I'' jr I rs-0,9 x-9 Jx-g

4" 8 BidnBidb: U=-x-+Zx-z

144 ^^

15!l135 ' s

47g.

t, xt t .0, L*/ =.8 \lr

BiAnoqiAb:9,6. > o,

^olt

_at-_

o' I'= 1' 11 '= ''. (0, 1t, [x+oi lr+0: \ s = '[V-; )rs )e >oir.3- x=ot I.)=0:x=0rr ltrc ..r:(x

3) v=

[0:1]:

z-1*9,2--!*l'6. x+6 x-2 x+6 x-2

2tx-Gtlx 2\ x,2+9x+54 ^ 2x +8x 24 x +2+9r 54 -^ (n 6Xx 2) k 4 6ttx 2) 2t'z+16x+32,r':+8ir+16 l'+6)lx-2) -"' (x+6Xx-2r - ' tx-4t'z .o.r-{ -i 6)J{2:rF,. rr+6)(x-2)

35o

ii:i: AITEEPA Mep3ns( A. r. ra iH. AKaAeMi,{Hur piaegs

!ii::l:lillril::t

et -!!:-J2x+s= Jr+10

Jr + 10: o.tr3:

r+10>0. 2"r+3:0i

.r:

-1.5.

12 J,r I0 J2,r-Bi - 144 24-x+tO=2x.3t _j-t+lt Jr+10 1a!.^ , - tz -- o, L'"".:tu .oi xt=-li.t" 26. t+to '+lo Bi0no6iAb: l. 481.1) \ft2t + 3Xr -4) = r'4t (2x + s)(, - 4) = / - 8, + 16; 2x,-5t 12 r'+8r-16=0; rz + 3:t - 28 = Oi t.\ = 7tx,=4. ll= 11 {erpaBlrnbHo; t, flepeBipKs: r,= t;.,!1u+ly tE=-7-4t 4; 0 O rpaBEnlno. = u@+a1a-a=a

i I

= 4;

BiAnoaiAh:4-

::Itl:a:ttiil{i: ATTEEPA Mep3nsK A. r. ra

iH.

AKaaeMieHti piBeHb :::::;: 351

1@ zyz" 11+z="; ,ft" - s' + to = r - 2, 2t' -

. 5r + 6 = 0; xt= 3t t2=

flepelipHa:

ztto rl+2=3; 3=3

gx + ro =

4x+4i

ax,-2Or 12 x,-4x-4=Oi7x, 24l

16=OiD=1O24i

rpaBvnbHoi

repeBipxa:.r,=-;,

xt=-!, r"=n.

al O*zlJr" t zo=a"+n; O+z\nlVl"-m -6('+2)=0;

;',r ir-B;=rV ; HeMacaMi.ry: ," = e; Js + ^11 = zJa; 4 = 4 rpalsn6*o. BiAno6iA6:4, 4'[v 2', u$, a =,fs- *,', z z.[x + zxsx + 21. 31 7 = 8 - x:

tx-2)lJ.r' -ir-20 -61= 0: l .-

zu@ +

r1s"

l2x' +

528 + 56

2yt -

"G z; 161-g

s1 + z =

a2=

',=

rpaB,,nBiro.

BiAnBiAb: 2: 3.

lx=

x=-2-

Ir 2 o, lx 2. x' x zo 6t Lr' -x-20=36t l'l

lx=-7' lr=6. IlepeBipKai x= z; ( z+2)Jl+2 2O--12+12 O J-14= 0 x = 7i ( 7 +2\J4s+7 20 = 42+12:, -30 = -30 - rpaBnnbEo; ;r = 8; (a + z).,6a 810 = 48 + 12; 60 = 60 - rpaBrrnbEo. 56=O:

.lt t' + tr,F - s' - s = x - r: tx+l)(Jx -rr..5 l' = -t, lir.l U, x I.

_ | tr lJr'? sx+s=l: '' x'-5.r+5=1; I

aez.9

*,.J,\

=,*t; t*'.[V*u=

+2r+1;

o^ l-.

24t, +

BiAn6iAh: Ot 5.

\E;;.8=

f"=o. I

'F-u

-2,

r-----i.::: Vl 0V0' 24 0 ,=7,,81716 24=? 1; 6=6 fiepeBjpxa: r. =

rpaBrrlLgo.

BiAno?iab: 7.

zt+t+zJ@x+t11x-4+@-s)=4xl r) Jz' +l + "Gl =2Ja; 2J2! - 5x - 3 = t + 2t 4(2x' - 5t - 3\ = x2 + 4x + 4;

+83.

352 ill: AJfrEEPA

Mep3rrK A. f. ra

iH. AKaaeMiqHrai piBeHb

t::::::l::::l

::::5T':'.,q

4Ox

=O:3"r) 5r_ 0;r,tlc rt, =0,

I, L3 I

r . 0: 2J 1 JL = J-, - He Mac rMicry; zJ-a ,[9=./-* -HeMaeiM,cry. !3 ! 3

fiepeBipKa:

*=-1, 3 BiA no6iA

4a4,D

rlel.N.ae

KopeEi3,

Jt I>4i o,[3:r-I>0i.r>1.,-

BiAnosiAb: (17;

t;1+"'["' u=,"-2"+t; ,(.h"-u-"+z)=o:

' l'=o. [,=o. (' 24 x" ax a: t.

.il:':.:itl!

q 2,8 -1-J;-=\E4: 2&' r=.r7a+lia. a@z li = t - g a 21p - 1gr + g + x 1i lzt - 4 - 2x + 10 = 2.rF - 19, + g. fi'+A=z,,lV -tor+s; 5r+a-.,f' 19**9; 25.r, + 30x+9=.r,- tox+

'Jit24=t'*2t:

xt2i x'-24=x -a"r'a: l'=:' lr 5. rrepeBiprca: , = o; Jr * on6; * z+ = 0 + 1; 1 = 1 - rpaBrnbno; , = s; JI;;J%;A= s+1; 6 = 6 - xpaB{xbdo.

-------u

rpalrnE*o;

3=3

BidnBidb:2.

npaBr.r,rBrro;

-l|' l;4.

o "("r-24-*-2J=0, l' L'lx' zt 'lt

7x 2 2\\5!'-13x -2i 4gx, 28x r 4 = 4tt5r? - t}x 2): 4gx! 28x 4.6Ox,- 52x-8illJ, 24x 4=O: D=400; x. - 2,, r"=2. ' 11 flepenipxa:,, = z; 1= 1 npaBsnLgo; 2EoTt2 "E "ll2 "E; .r. ='_: .i--l-.i .l--I ' 11 vl1 -HeMa€3vicry. Vll vU

x I: 2vl 5-s 2: i = 2 - npae,{,rsHo: r - 4: 5Jl6 20 5 5i 5 5 npaBx,rbHo. Bidnosidb:

55 =

'lJ

.0r

HeMa€ BMicryi

1"-4. +:+S = -1+ l;

42r

'6; '[ bbFiEs6Es91672bt6 _ '' ' 13 \113 ll 13 13 Jra Jls JrB Jlt Jlg BiAnosiAb: -1. 4 "tE' 1-$r-=Jr-7; 5x-1 z.!1sr-tysx-4+u z=r-t;

IepeBipRa:, = -r; (-r + r)rf-rf

r, = -r;

lepeBipxa:

7,8,

BiAnosiAb:

n = -t - 5r 4(3! + 13r + 14) = 1 + 1Or + 25r,i - 1 - l0x - 25e - Oi L31c, + 425 + 55 = 0t 13x, -

E. ' = r, *.. = 13

4624..

x"^ x

+*\.

2l "G l<at OA3:r>1:x-lrt6ix.

Bi1no1iAb: (1i 17\.

1> 17

161

17.

(rrq..l---: 17

q It I > -4; oc*irr,Iir KopiEE ap[ibMerr.:.rnr.ri, ro r , .ruc,ro, sfie Ba,qoBonbHse OAB,r€[1;+-). BiAnosi1b: 11; +-\. 4\ < 4, I{opeHiB EeMae. "!;fr- ,'^ t-\r 4a5.1\ J2x-4 >Js --r: oA3r l:" I -* 1-'l're tz;sl.

2t 4>5-ri3x>9;x>3.lr-.r>ui lrss: RiOnosiAb: te (3,51.

ii*ltili{1i:l l2

yci rAE r0

tTrrrrt>)"\i+ 2 A 5 '

AITEEPA Mep3nrKA. r. ra iH. AKaaeMi,{Hr4i piBeflb

s.,r.

l::t:

3Sg

zt G<'6+r;

oA3:

BiAnoeidb:te[O;+*\-

I*'0.

,r> 0; x < r + l; 0 < 1 - npaBlrnlHo.

[r+1>0;

[ 1;0,u 9;1 . It s).,,/i'+a'+:<z'+r; OA3:r'+3r+3>0;r€fi. BiAnoeiAb:

+' < nlVi OA3:t'9+r>0; t(t+ 1)>0; ,.r=0; t,=-1; r € (--; 1l u [0; +*). t'+t<x'+1tl.<1. BiAnoqiAb: t E ( -; -11 ut0; 1). q nF a,*t , Jz' z; O

Jx"

lr':-lr+t:0.

ls*.6 l

ire I i+' Il2r 3:0: | 2 x' 3'+1>21 3;t2 5x+4>0t \= 1; r,= 4: r e (4; +-\-

O-tr3:

Bi.Anosiqb: (4:

"1,2 r'+3x+3<4r,+4r+1: 3r'+r-2 >0;r:,= 1; '3 2 firrrro2x+1>o,

)

eionoaiao:

a; .li

+-).

:,.

sl .,6: r' > G, - ro;

ls s"

On3: I

"r€( -i

-4 1,6

|_8l

EeMa€ nopeHiB;

41.

-4

qA6,

", oj

( -;

J24-

OI\g: 24

'xrr'

51t

2 O, :(

4,81;

4,8i

- 24 O,

\ /--=-\ -'----*-\" 8 :0

'--- -

:t:n 3 48

D J2t{+7 sr+2ion3:2r + 7 > 0; ir > -3,5: a) J]Ku{or+ 2>0tt> 2;%c+7<x'+4x+41 x2+2x 3>O.x,= 3:r,= 1ir€[1; +-). 6) sKrr{o , + 2 < 0, )c < 2, HopeEiB HeMa€. +*).

J3r r'<l-r; OA3: 3n t'> 0; r. = o; ir = 3; ,c e [0; 3]. .flllnlo 4 ,> 0; t<4, BpaxoByr.rt OA3, J'€ 3)

BianoqiAb: tO; 31.

l1 e -

:n[:7;

o,(3: 1 J" > 0; rL = 1;

.flrtrqo 3" - , > 0; t < 3; I 9 - 6r + ir'> I -gr'!: 10t'

(5r.'- 3t)

354

o; J.(sr

- 3)'0;

6jr+t:> 9(1 6t > 0i

7:t = 6 <O; ).\ =

l: x,-

1,5;

r € ( -; +*),

BpaxoByroq{ OAA

r € [1; 6].

J2 r>r.; O,[3:2 :]r>0irs1: rlrli{or>0,.to2 x>t2,xr+t 2<0:

( *;1\. 4 Jr.+7>x+1; OABir+7>Otx> 7i a) sftqo r+ 1> 0; r> 1, ro x + 7 >x2 + 2x+7i r'?+r-6s0; r,= 3;x"=2; re [ 1;2]. 6) sxqo r + 1 < O; r < -1; rel7) 1\. -Bi1noqiAb: | 7;21. :t J*' r.x: O,[J:r ] -O:r., I:r =lr j' € (-*i -11 u [1; +-) | a) nlturo r > 0, ro a, - 1 > x,t 1> 0 Henpa Bi0no6iAb:

BiAnoqidb: (3t 4,41.

BiAno6iAb: 11;

t:t = 2; jd2= 1; x e [0; 1). 6) nlirrro r. < 0, ro jr € (--; 0).

u [2j +-).

t 5x 24 - 5.ri fltsLro ir - 0. 'ro = -8,; r" = S; r € (3; o. Hcllaa. po3B s3KiB. on,.o i

6 >Ot x,

4e7.1,

lr': 3r+2>0. x(l__;rlrrl2; t ll -_). on3:1,, [2x'-3.r+1>0: \ 2] x' 3L + 2 <2r'- 3t + l; t'- I> Ot

BianoqiAb:

. z' + z; ogz, 7! - :.'

7x r' 6<4r,+i2x+ 9; 5r,+ 5ir+15=0; *+x+3>0; r)+.r+3=0; D= 11;

J" z,*z.'ti"\z,-tt

-)l .

Bi0no6iAb: 11; 61.

'ic>

Bi1noeiAb:

€ [1; 6].

fiI{rro2r+ 3<0; r> 41.

L.r'-16>0i t'1 - l6i x' + 5, - 24<ot

'-'

?t \it I

[0;3].

re[ 1;1]. ', =1;

jc'?);

aiit:AITEEPA Mep3ncKA. r. ra iH. AKaAeMi'{Hnr pieeuu :i:iji:i!il:.il:iiii'i:}

1t =N-=-Vttt

Br'rnbrio, HeMae po3B'.{ariiB;

6).rxrqo jr < 0, ro r € BiAnMiAb: ( -t ll.

(--;

11.

q ulV-zr>s 4 oA3:.r,

zrc > o: xtx (--; 0l Lr [2; +*): a) nEtrro 4 ir > 0; r <,1, ro x'z - 2x>16 8! + x,; bc>16, I 2 f t x> j: r)2-. raaoBoi6H'c on3r r. Lr;: 6) nnqo 4 jr < 0, r > 4, ro ir € (4; +-). sia,..ia,, lz?, * *).

2\ > o:

,. €

= ot

r=2t

" """'4""'-

'.'."""""'.'a:,i,1.tr.a..| l.:a i a.. --....

'3 "i

)

sl ,["\ 2,'; o,qB: J., + jr 2>o;r,= 2; ,- 2i x e' ( -; -21 \-r [1; +-): 1x -2 a) nnqo r > 0, to x, + x - 2 > !.t t - 2 > 0; r> 2; x> 2 aaAoBonllrse OA3. :ttii::{iiltiii ArrE6PA Mep3neK A. r. ra iH. AKaaeMi,rHran piBeHh lr:::

:..*..-.\--Vz;

12"

3S5

sRqo

r < 0, ror€ ( -; -21. F*; 2l u (2; +-).

BiAnosiAb:

6) v/ ;'-;r. 5 8 2.r: oA3: -I r 61 5:0; ,r' 6.r=5<0:.r,' 5:.y, l:.rc t1; 5l: a) r1.llro 8 2r ? b; r. : 4', .ro -t:z+6:.-5>64 32x + 4r,; -5t, + A8x 69>0, 5x? -38,r ' 69 0i .r.r. 4.6: x, 4i r E t}i 4j. 6) flHqo 8 2,r 0: "r 4. ro,r < (4; Sl.

BiAnoqiAb:

- F=\

Y I

,-.----\

Y 5

51.

4. TPl,lrOHOMETPllgHt OyHKqti

1. BracrllBocri TpraroHoMerph,{Hrx OyHKqit 488. Pa4ianny Mipy Mo}t(na o6qHcnur?r r a oopMyJroro

,. r! 25" 5n 180" 36 tr ' 1600 8rr. 4) 180. I

-. n.100" 3)

-. r 40" 2,r 180" 90 -. n-21O' 7ft 180. 6

180.

5rr

n.300" 5r

1ao.

497.

489, 3arrictr n cd,q niAcraBrrv 180..

t) ti8'=

4) 49o.

tt"

4 2!3!:

1,2 . 180. = 216.; IpaAycEa

3) 1qq

=72".

5)3.1800=5400;

10"

36.

80"

PsAiaEBa

Mipa ltyra

6) 2,5. 180" =.450..

108"

105. 711

t i

= 20".

720. 5n

824 1,8rr

240. 4n

49-1. AoB}ri4Ea Ayrn nona o6qrcnro€rbcs sa OopMynoro I Ro. =

|.tz

a" 6*1;

2)2.12=24(c.M);

3) 5n 12 lon (cu)t 4l2fi t2 .24filc{t. "-= 492, 1) I = Rctt I = 3. 5 = 15 (cM); 2\

I=J19 =4,sn

1"*1.

3)Z=0,81!(cM).

493.r=3,14pa{.

U!-t,rz; |rt,s; a1 r,Os r r; 1r 1' 4s4. 1) o,7a5 -,

356

X.t

z)-t,52 4) 4,71

>-z;

-!;.

<4,8.+<4,8.

O,r.

O,SZ;

Itl: AITEEPA Mep3rcKA. r. ra

iH.

-\, -! AKaAeMi,{Hri pieerr :i:}j!{Lll{:i:}j.:-:l

III

.rBeprb;

2) I .rBeprb; 3) Iv 'rBeprb; 4) III qBeprb; 5) II .rBeprE; 6) I qBeprb; 7) 600" = 360" + 240", III qBeprbj 8) ?50" =360' 2 + 30", Iqseprb; 9) Iv 'rBeprE;

10) I .rBeprb;

11) 400" = 360' - 40'r-IV.rBeprE; 12, -470'- 360'- 110', III.rBepr6; 13) I .rBeprL; 14) III 'rBepr6; 15) II qBeprb; 16) II 'rBeprbi 17) -1,8t! = -5,652, I.rBeprb; La, 2,4n=7,536=6,28 + 1,265, I qBepr6; 19) 2,6r! = 8,164 = 6,28 + 1,884, II.rBeprb; 20) -4,25; II .rBeprb; 21) III qBeprb; 22) IV'rBeprb; 23) III qBeprE; 24\ 7 = 6,28 + O,72,I '<septs.

.rBeprb

(90";180')

( 180';

2?0")

(1,57;3,14)

III

.rBeprE

(180";270') ( 180"; -90") (3,14i 4,71)

IY qreprr, (270";360")

(-90'; 0")

(4,71t6,28).

498. 1) II .rBeprb; 2) II qBeprb; 3) III .rBeprb; 4) UI s8eprb: 5) -380" = -360' - 20", IV trBeprr,i 6) 700" - 360'+ 340", IV qBeprB; ?) -800'= -720'- 80o, IY qleprbi

.j.Iia:i:i:::j:iji: ATTEEPA MepsreKA. f. ra iH. AKa[eMi,{Hxi piBeHb

ii:i 357

5O7.

8) II .rBeprb; 9) III .{Bepr6;

lO) 11) I2l 13) 14) 15)

7n - 33= -Ztt . lv vaePrb; 5,5n - 4n + 1,5tr, IIe Eanencnr6 ,{oqEiil qBepri; ij = 2n + -:. I qBeDrL; 6ti

(

(o;

2) (-1i 0)i 5) (0; 1);

1);

I Ityr

2jr paaiaE;

Etl',.t'. 2t + 3t +

5x = ni

TH\r -::'3nIT K)l 'itu2

to,

3) 6)

xvr = u t= 2, 10 3,

paaian;

(0;

(-1;0);

(0; 1); ( 1; 0).

III Itvr

5n paaiaE MaeMo piB-

l4n 15

oAsoMy

trpr l|oniEin

cvMa 3ocsi nix RvriB' v3'rIrx 15 = +. 15 " +: Bepu' i - 2r. n=2n: *4=15 ' n= 15' 15

504. KyTnpuorHoBi prBBo6erpPHororovts)rHYKa{180'-36"r:2=72':3ti" 2n

36 n 'r,16"5:

2n 2fi

-1040'=-360'3+40';

2) 180" ra -r80'; 4) 360' ra -360".

40';

680"

= 360'

2) 510" = 360" + 15O'; 870'= 360" 2 + 150"; 1230'=

360'

40'i

3 + 150';

-210'=-360'+150'

358

= 3.

po"r,"uu.",

_4 l0 9x. r3r-t{r i} 4r t0 9,(. x-2 " -2x )t!.2t x\x 2)' 3:t'-6x x+2 41 10 9:,r 3irJ 11ir + 2 10 9r. =,@ 4: x1x - ,k-4 = 1(r 4t 4 rr,+z=ro-s,, [a''

\ ?r-l x

zy + o.

PorB n)l{FMo

Il BiAnoaila: !.

PoJB slr.Fvo

3n 2r - 8 x , Oi x , Z.

BHenEq:

t00:

2: r..

p'B-AHHn:

51'l " Hexan 40

- nirbllicr!

o. ql ,

nporflrlarr

MerIKaHqiB, rqo

qa.\,,o piBJnHH,, 88

,50.] '8a 200 Ao 1,1025jA0=A0000. =

polir roMy.

200 4 I , , ,i;J

,4^ = g8 200.

512. 1) 2 cos 0o + 3 sin 90'= 2. 1 + 3 1= 5; 2) 4ts180' 2ctg90'=4.0 2 0=0; 3) sin,15o +

cos45.=

i::i:aITEEPA Mep3nr( a. f. ra iH. AKaaeMi'{Hui piEeHb

::::::::::::::::::::::::::::

ta + fa = Jt:

,:i ,:)'=l

sn.6o.+.os30

sin45"cos45'crsso. =

6) sin0"+tgn-sh4=

506. 1) 400'= 360'+ 40"; -320'= -360" +

90" + 360"n,

Bianoeiab:15.

5O5. 1) 90" ra 270'; 3) 270" ra -90';

Z; Zi

Birro6tab.. 80 000 MernaHqiB.

5o3. soBsiusili Kyr Mlroro&y?sq(a

l'1,

5102 -. 7a paAiaH; III Rvr 4' pa'qiaE; IV l(vr pa,qialIl II ICvr 5O2. Heran I llyr - 3t - r paAiaE. CyMa BsyrpiruEix RvriB 'IorrpnryrErlra 27r pa{iaH' MaeMo piBHtHIIE: 2]. r + 3t + 4t = 7r = 2n; 15x = zn; x = 15 l4t1 8n "' 2,t --. 2n lKVr -r; IIHYr- -:tUKYr15 15 BidnaBidb: l5

BiAnoeiAb: 2.

.^: lllr{Yr

2T 8n 5' 15'

e Zi

36O"n, n

sro.rr x q= ,l: , ]', 6=x. ],. -ir 6=0. ir3 x3 [r_3,0: lx 3=0. P-o3!'frrrcMo I piBHsdHs MeroAoM riA6opy: r: - r 6 = 0; a, = U piBHrHHe. orprMa.vo { = 3.

1);

r3trr i BtAnoaidb: :

4, 2800.

2) a= 60" + 36O.n, n e Z. 3) o= 135"+360"n,neZi 3) 6)

1i 0);

5) (0; 1); 8) (1; 0).

4) (-1; 0);

5O1. Hexan

(

4) 1i 0); 7) (0; 1); 5OO. 1)

5O9. 1)

qrepr6; 1);

45";

4)a-135'+36O"n,neZ,

IV 'rBeprB.

499. 1) (0;

0= 90" +

2) a= la0'+ 36O"n, 3) o= 30" .360"n,

.IBepr6;

III

1t80": 2) 190';

5OB- 1)

i=l

,,,

* ; n = *,

0+o

(-1)=1j

3tr

tcosn + 4cos + 2cos2,r = -5 + 0 +2=

6sin.1 zcosl + tgI -7cts!=g 1+1-7

z"r",l *".",1 4

= -4:

€l'

4l' \.2) -l\ 2l =r*1=r1, 44

:.1

iii::i::.::'ii!::ii AnrEEpA Mep3nc(A. f. ra

iH.

AKaseMieHhi piBeflb

ii:l

359

lac

n","n l=1. ror shrts, l'.ut. 2a .'' ---'3'- 6-'6 =@.1-.] 2 lJ3.l

517. OcKinbns Y3

513. 1) sin 270'- 3 cos 180" = -l 21 '

"."6s"

1* 1= "i,'3s" = 22

3IIaqeE

I t+1 2sin1 2! 62 . 'rcos-.crs3 Js zJs ,E. srn4 " .-" JE t, Z 'E Z Z=t.l

7')

*"1 "t"! r.tc!= o+1+o=

6cos0+4.sin2r'

llle-(

Ille

lf]'

3).

519. 1)-1 scos q< 1; -5 < 5 cos([< 5; Haii6inbue b; EanMeII e- (-S); 2) cogo - 2i 1< cos a < 1; -3 < cos a - 1s -1;- sai6inbme (-1); IIanMeE-

=u-

f.'

(-3);

3) 0<sin'2d<1;5<5 +sin,d<6; Eaii6irbrre 6; EafiMeHr[e b; 4) -1 <sir d< l; -3< 3 sin a<3;4< ? - 3 sina< 10; lafi6i,rbure

=6+0. n

MoJrtyrs.

MeH'tr€

10.

4; sai_

gtr 5n xxl r: r.. T: =n , zn -,7, ' --4ft= z '- Z 2i 3n n .-n+2n 2) sinx= li *,=-I. xs=-2 4\=-.7n . 2 *" 2i 521. 1) cos .r = 1; xt - 0; tz = 2ni ri = 4n 2) cos r = -1; ,r=nix2=n+2T=3n;as=tr+4n=5n.

52o. l, sin.r =

514.

"t'(

515.

2ai

518. 1) -1 < sin a < l; -3 s 3 sin c{ < 3; Hai6i{bme HafiM€nIIIe (-B); - 3;IIsriMeIIme 2) -1 <cosd<1;3<4+cosc[s5;Han6inbue-b; _- B; 3) -1 <sincr< l; -1 <-sin&<1t1<2-sind<g;Eai6inErEe_B; HaftMeIIrre lj 4) 6- 2cos s; -1< cos d < 1; -2s6 2 coso<8; Hai6inbrre _ -8; 'IaiiMeEi[e 4; 5) 0 < sin'zs < 1; Hari6irEue 1; IrajtMeEltre O; - 2; 3<2 cos, a- < 6) 0 s cos", o< 1; 0< 2 cos,o< (-1); EaiiMeI{-1; Hai6inEllle

bl- "tnl+cosn+ts]

4sin'?

+ 3 = 2;

7 te2 45" - 3 cts 45' = 7 - 3 = 4) 4) sin 180'cos 120" tg 60" = 0 cos 120'tg 60'= 0;

'-.'----- "' !.1 2 = 1.t2, ro 3flaqoHsa sin Ct, cos o }re Moxyrr " qopissrcearl,l z', tg (,, ctg

, Il=.:nn.@.o.rr, 3 2 6)

sin 2d. 6 z l=t; 2 (^ - "v": "t; '11 6t "*"2 =0: Scosj'6 - 2 cosBc' 3 cosc. zsin 1=

sinoi

E=:

522. 1'

1)'442 sin4.n sinn=0; qsinft

'n 9=zJzr sin4P' 4sinp' 4i ts4pr 4isp. 2\'' qq L= rgr '4 4 ' o; 41gI=4.t r: y e [-1; 11. t: y € [-1; 11. O6nec1l 3Ea.relr, y = tg rr y € (--; +-). O6.racrs sEaqelrl, Y = ctg t: Y € ( -; +-).

516. O6nacrE sra.reEr, y = sin O6"racrr, axavenr y = cos

-4- -u'9/. z) ./is =

\4 12) '4 ",nfr-11*,r,3 . /n n)

"'"1

523.

sin

7) piBnic$ MofinlrBa; 8) piBnicrb Moxn sa.

3'ul

sin

Brr

i,:

5n ol"rnln nl ,ni

t'rtu

Va.n[J-11 ,"0*"1 J-.n^] ,6"rnn.,Jzcosr t)

rnn",'n -4 -6

9rr

I JB

'*,

t; ./^n) r fl !5 -3 6,/ 6 \ _ "r"; _1-+_, JE 1+ 3 4 ll ,.,"1 r.1* r.lJ cosr Bsin4 -"(t \

;

piBet" ll.t*l:jtii:liii:i

a + 3.1 1+r 1r 1222

"\12 6/ -\3 6)

- -1t= u.-_-_ /60, prBErcrl MoxJrtrBai 5l ot 9-rl. DiBEicri, Heaaoxnr.rBa: 88 ll.::iAJTTEEPA Mep3rqKA. r. ra iB. AKaaeMieHxr

srn +cos 1+0 1

/n nl +cos /r , n\ aln -+cos3n=_L=o. I +1, srnl \36r!36i662 I n-"'';,l n\" ^. I st' 1+ n\"-|."'" 3) , z"r' -"". -"',, = ; "," ;J i ; "r., f [":" f I

prBEicrb HeMoxr'lqBai

3) -V1J = -1,06, piBgicr" EeMoilc,::lBa; 4l 1= 1.05. Dilnicrr, HeMonrnrBai

360

=2"i"[.i'i-"i",' =a"r'["r'i

€t-1i U, pisuicrl, MoxnrBa;

;

iinz.I44+ "o"2

iliJitilitliii

! 3

AITEEPA Mep3nrK A. r. ra iH. AKaaeMiqHur piBeHb

,!j:: 36i

524. 1) sin x = 2r'2sin

t: .r

531.1)

+ znn, n e Li

-znr,

525. 1) cos I = 1; t = 2nn, n e Z; 2) cosr.= 1; x=n + 2nn, n e Z.

: I .osr\ l:-1 :-cos,r. tlO. I cos.r:2; I I [] \ <+-.r€ -t ' -:+-l2 l-cosx 2 ) 1-cosr

9 -laroEx' li I / .cos.r:1:2:3 !;:-;: l1 1 I < 2 aL rLt_:tt: 11 I " L2 ) 4 3 cosr -!_t 2 2 3-eosx I 2J g ., -1 :sin,rl liO<srnr 112;

532. l)y

BiAnosiAb: se tcEye.

3)cosr=d'-1,

1<a'

=2. [" " t:' t.1r ],a'>oi Lr'

4) sin jr=a'

fo' a-s l.

It 4<a< liael4.

2l..

1<\i -,t2,

Llle,Q:

a-1;1<a'

J2..

", I Jz,,El,

a-7<1;

\,'-----\,--; .jppir;

fa' a -z<o. 1<

5a-4 '0. sa+5: t, o _ lrr 2l! l3r 4l: I;5d+5i-1; ld'-54+620: Ld'? at2 i a+2. 6\ lFt " -02 2i-1<a 2<!; 1<a<3; a€ [1; 3]; 524. 1)sint=a 0, ro l asxx rHaqeqb r JJe irH) c: 2) cos r = a' + 2; ocllinEnrl a'9> 0; d:-2 3) cosr=a'-3; 1<a' 3<1; +so.

lo' e--t, lo'-z-0, ".1-z; "E)ul"E;z); si,n rc=2a a'=2i 1<2a

a' - 2 < 1; '1 < a2 - 2a + 2 < 1; t 0. ra lr'z' 0. !'=t' , ,. 2a 2a-2't. o" lo . )a 2atBzo: la - 2,r3-0: o'R: \o'-za.r.-r

ct - sin'd = sin(2 rr sin'a . 0i 2 sir c' sin: o.

529- OcIlirLRr 2 sin 2 sin

sin cr); sin ct > 0;

sin c[) > 0' ro

53O. SEaiiAeMo ssaK pi3El-rqi cos 10" - cos 10' cos 20'= cos 10'(1 - cos 20')' cos 10" > 0; (1 - cos 20") > b, ot*"' cos 10' cos 10" cos 20' > 0; co.s 10" > cos 10' cos 20'. ra iH. AKaAeMiqHl4i pieeru :;:;1!::::;i:i:i:i::i;i:i

sin s =.-(-sin

a'-3<1. fo'

). O

&yr - nporrr roanr {nroBor crplnril, Bln IIe-

cosl -a \2

a' - 5a = 5 31:

cosri4:

)

oc,= oct,

€ [-1; 0] u [1;2]; - 5a + \

5) cos n = d'?

peiiAe B.npnMol(yrHl{n OC,BD,,

la'-o>o; a

1 lr s;n,1--i a'l2t

533. npu noBopori OC,AD, EaBKo,ro roqna

a ot_,,

l' srnr:l; I s2 sinx'3:

Z\ y=: "

526.9 tgr.r D(lg'): x ' - rn.nr/i A = cLg kt D(cl'g t\t t t n + n' n eZ' + 3: -1 < a + 3 < 2) sin n = a' + a; a' = 0; rt = 0;

1 . r, -,,.11, rl, 1. 3 2+sin,r L3 l

-Z-

527 . 1) cos x. = a

y=Z_"i.,,

(:r);

sin

to(i

OD, =

OD2= OD\t

-q.

-sino;

= sin d.

,qoBeAeHo.

534. npl, troBopori

OClAD1 HaBKono roqrtlr O Ea K!-r'rr trpo1h ronhHHrr{oBoi crpirxx BiH nepefiac B npflMonyrrrr& OC,BD,, ,roni OC,- OCJ OD,= 04. cos(n + rr) = ts = -OC, = :OCt- t^= cos 6., cos d = ( cos c{); cos c[ = cos o. AoBeAeEo.

535. 1) -A(r; y) e I qBepri; jr > 0; y > 0; 2) A(ti y) e II qBepri; r < 0; y > 0; 3, A(x: V) E III .rBepri; n < 0; a < 0i 4) A(x) vte IV.rBep"i; r>0; u <0. 536.

ll/lx) t'

2h-_

Un: x--5:r.=5-

flrvprp

qHa eraHocuo roqR}i O:

xt3

: r'nannar , r1;= 2-t " " z) f(4= lx": ,(Dr R; crMerpu.rHa BiaEocHo roqlrr o; r( r) = iF l' = -i,F, lenapra; sl f @) - dV; ,(Di -a; crMerplrqtra Biagocgo rorrxr.r o;

r(,)=i/Gt=tr?, rap'a; a, f@\ = 2r7 + 4x5 - 3'; ,(D: R; ctrMe"p@Fa Biasocno roqr$r o; f( x)=2(-x\1 +4( ')5 3( r)= 2t7 - 4x5 + 3r = -(2x1 +4'5 3r), i::iiiitiiiii{i:

AITEEPA Mep3neK A. r. ra iH. AxaaeMiqHnfi piBeHb

EenapHa;

i::i:

063

DU): .t t 0t x z 2i x = 2. 5) ft,rt = -;l-; Y' - 4v' 55 napFa; .-i, ''l(- t\

cl{MerpL{'IHa BiAHocHo rot{Rlr Oi

i/rl; D(r: li; cxMerpr.rHa fr xr=t4l fi. *0''". =

sxs(-i)

2. 3HaKr4 3HaqeHbrp1,lroHoMerprl'{H1'!xOyHKLlii 534. 1) sin 110' > 0; 537. 1) 38" € I cBepri; 2) cos 200" < 0; 2) 119" € II 'rBepri; 3) tg 160' < 0; 3) 196' € III'rBepri; 4\ ctg 22o' > 0: 4) 302' € IV qBepri; 5) sin (-280') > 0; 5) 217'€ III .rBepri; 6) cos 340" > 0; 6) -74' € IV csepri; 7) ts (-75') < 0; ?) -98' € III 'rBepri; 2n 9) -- € lqBepfli

tor 91 e rI

qneori;

7,t F tll t:r'4 !! e Iv

lll

qBeDTr:

qseorir

rrt -4 e lll l4r

!I e r

onepri:

o = z;

r,5+0,25-0,75 Jz

2."tE 2

+ cos(

45")+2sin(

30".) +

6cos(-60")

= **9-r.!ru 2222

tz=2-Ji:

sjn'z(-60.) + cos'z(-SO")

1n' toa<o: "6

ll.,*1 rt zt"J rssinl-Il-q"osf 1l=z r-rr (-Js) Fs.r-r)+4.Jq= --'-'-' -t 4t -t -o1 6) \2) i6i 2

16)

cos

Yl +L'"Ei =""'" \2) \2

3 s 6 ,-

=zn6-a+zJ5=d5-a.

<U.

544. 1) sin100' > 0; sin132' > 0; sin100.. sin132" > 0;

539. 1) sin 186' < 0; 2) ts 104' < 0; 3) €os 220' < 0; 4) cts 340" < 0; 5) sin( 36") < 0; 6) cos( 78') > 0; 7) ts( 100') > 0; 8) cte( 2s1') > 0;

9) sina 7

2) cos210" < 0; sin115" > 0; cos210'sin115. < 0; 3) cos285" > 0; cos(-31q') = cos316o > 0; cos285..cos(-316.) 4) te112'< 0i sin165">0; tg112..sir165"<0; 5) cos318'> 0; ig(-214") < 0; cos318"tg( 214") < 0;

> o:

/ r 3n\r 11) cosl- 12 < u: J r e"l t2\ .to/ _-t>u.

541.1) cosl-60"t- re(-45"1 .os60" tg45"=

a) 6

cos{ 3Ol = -cos3o" =

iH.

t, ,=-fr,

2r ctg(-60)sin(-45")cos(-4s'l cts60"sin45'.os45"={ Mep3rlrKA. r. ra

2) sin134"

3) ctg(-45') = -ctg 45' = -1;

< 0.

545. 1) sin102" > 0; cos350'>

12)

-!5i

> 0;

6) ctg300'< 0; sin220"<0; ctg300'.sin220. > 0; 7) sinl>0! cos2<0; sinlcos2<0: 8) sinS<0; tgs<0; sin5tg5>0; 9) sinS>0; cos4<0; tg5<0; sinScosStgs>0; 10) sin(-118)<O; cos118'<0; tg118"<0; sin(-118")cos118" tg1la"

> 0:

ror tE9I "a

I = -sin30" = -!;

!1{: ATTEEPA

12\ cte L,7 < O; 13) tg 1> 0; 7ft 14) ctgt < ui

15) - o e lqBeprr.

964

1 + a. r +

,.."(-:)

543.1) ssin(-45')

qseDril

2) te(-60") - -tg6o"

-2.

./ nl ,.r.lrl'-l@1" \ 6l \2) \2)

rJi

l) sin(-30')

= s. o

ri.* =t.{,

Jz2

16n

54O,

r"*[-;) -.-"f-;)

"t"(-;). 2""<'r. n"''(-;J ='6 G * z. ca * a (@

.,( n\ Lb+srn'l--l-cos-l I 6/

4',

10) cos2<0; 11) sin (-3) > 0;

z.r+$

=3 2+4.::=4i

8) cts (-230") < 0; 9) sin (-130') < 0;

8) -285"€ I.IBePri;

ts(-4b.) + cos( +st = -f,+

ro'{ti' o;

BiaEocEo

a stso + zsrn[-r)

t-xl'-4(-x)' x -ax'

o) /(r)

s42. 1) sin( s0) -

aKaaeMiqHnl pieexu ill:l:i{;}ii:i!i;i

cos

256"

4l cosl42'< 0; O; "inzz" O; "1"1=?. sin?2" 5) sin112'> 0; cos(-128') < 0; tg198. > 0; sin112.cos(-128.)ts198. < 0; 6) sin( 245) > 0; tg183" > 0; ctg(-190") > 0; sin(-245) tg 183" ctg(-190.) > O, s46.

9 + f

sin lsz"

0; sin102.cos350" > 0; 0i cos131" < 0; sin134.cos131" < 0; > 0i cos256.<0: "ll-.]jl. s, >

Ilsino!gc- 0i zt "in'-9.0, cosd

4) sin s -

[r:tlliltilll{i

cos o

> 0, ocRinL&Ir sin

3.1

"in'o.0, cosd

> 0i cos d > 0i

cos a

> 0; sin o + l-cos d) > 0.

AITEEPA Mep3rcKA. r. ra iH. AKaaeMiqHni pieexs

iill

gos

f sinB ,1 lEl . P 0: 2) " ,'0 r 0: srn li p .os 0. 4) sin 0 - cos 0 0. ocKiibK sin 0 0: 54a. 1) te 130'< 0; ts( 130") > 0; ig 130' < tg ( 130");

547. ll sin

P cos

555. lf /rr, = tg .r - .Lg xi Dlf\:.(?nk,*c Z; x t\+nn,ne/; 2 It xt tg.r - ctg n ttg -v ctg r1. n.nrp"u.

Dtht x , : . nh- h t- zi .in , tgt=0; "in"*r8'. srnx tgx 2 sin,r sinxrcosjr 1r _ ?u. /u. lsinx*O. lx, nn.n-7. stnr-cosl l'o'r ' r': lr '| znm'm' Li :::: - - ., ""_^2 -'" "_, s,n( "r)- te(--r) (sin/+Ls.r) sinr r{sJ. /' ' -. = sjn(-r) = = -*rr,r.z ' si", - tg r ' "ap"s' - ie(-r) Gi" r - ie ") cos( r) 3) /(f,) = :.''' : Dtn: !. !7i /'-x) = "i*, . nao,,,. ("-;t

2) /tr)

2) tq 110'< 0; tg 193'> 0; tg 110'< tg 193"i 3) cos 80" > 0i sin 330'< 0; cos 80" > sin 330";

ar 8n 4l sjn 60" 0: sin -" ' 0: srn 60' , .in i: ud ,n 5) .le 1' 0: .os 280" 0: .te:' cos280': :l

6) ctg 6 < 0; cte 6" > 0; ctg 6 < ctg 6". 549. 1) sin 200' < 0; sin ( 25o'.) > 0; sin 200" < sin ( 250"); 2) cig 100'< 0; ctg 80" > 0; ctg 100" < ctg 80'; 3) cos 250" < 0; cos 290'> o; cos 250" < cos 290'; 4) cos 6,2 > 0; sin 5 < 0; cos 6,2 > sin 5.

tt 1,n= t!''r, DO 5.1

55O,1)sino<0; sino sin(r =si c[+sin(r=2sino;

0; cos c, 3)tgc[>0;tgCr-tgq=0. 551. 1) sin B < 0; sin P + sin I = 0; 2)cosP>0; cos0 cosB=0; 3) cte li < 0i -ctg B ctg B = 2 ctg 9. 552. l) sin o 0: cos c 0: o . ll qBcpli: 2, sin d , 0: tg o 0: a L TTT qBFPri: 3) sine=sin.r; d € I qsepri a6o a e II qsepri; 2) cos q <

4) ctg

+ lctg la = 0;

cos & = -2 cos d;

€ II qsepri

a6o ct

l1r)=cos;r+f; ,(r:.R; l( r) = cos(-'l * i

u\ f@

=*#+a;

clgt

l\-x

(-.!)'-1

D(n:

)2 1)

r+ tt; '

nn, n

crs). (.r' - l) . x'-1

"o"

e z:

HenapHa.

G' 36=VtJrL; x, 36=2x- t;f ,2r Bb=O:11= .Et',=7, ', = 5; vE6-36 =J 10 1; ./:rt=J tr; aeMa€ sMicry; n,= ?; 36 = vt4 r, fis = "4t-

IlepeBiprca:

"{3.

Bi)no7iAb: 7.

1)coss>0;tgcl>0; d€ I'rBepri; 0: ctg L/ 0i c, - IV qBepri: 3) Lcos nl = cos cr; o € II .IBepri a6o (r € III 'rBepri; 4) ltg c4 ig d = 0; c, € I .rBepri a6o o € III'iBepri. 554. l) /(x) = sin'? r Dltt Rt ll r.) sin'{-rl sin ir' napHa. Le{ -x) Ls --.r r,aptsa. T lv)=:b-. D\l)t x . Ot /{ x) =:3) l(is) = tg + cos x) D(f)t x +71h, k e Zt f( r\=tCCt) + cos (-ir) = ' = -tg r + cos rc = (te ir - cos a). <f'yHllqin saranbHoro BltrrsAy. 4r /rxr-f "o"'. otn, I cos"r' 0; xtn-2nn,n'Z: I +.os r I - cos( x) 1- cosir naDlta, /l ' -rl 1+ cos( x) 1+ cosr -. (-'f + cos ( = -ri + cos 'rr. ovl{xqis + cos jr; ,(t: Il; l( 5) l(i') = ') ') = '3 ranBEoro Blrrns,ay.

r=r;

rb- Bx=:t, +2r + Lt f + Ex 14=o: '[r-ar=r+rt lepeBipxa: r,= z; -1Es+zt-t--7; 5=-7 - seirpaBu,,IEso; r, = 2; u/t51-1=z; 2=2 --EpaBo,nbEo. 4 \85-3'

553.

x, = -7; x2= 2.

2, sin a

366 lli

x-li , , | ^*.r-2,

556. 1)

€ IV'{Bepri.

ir sin.r D{/): I cosr'0; cos,r- Ir'r /nh.hcZl 6r /rxl= ^ 1 cosr : .rsin(-r) x sin,r ll-x)=-=I cos(-xl -I .osx . napHa' (r 1) ciii D(/): x - 1. ovHrq' Jaran6Horo Br.1c*av rr /rrr . -r-1 r sinr: Dtni',oi {-:rt s'nr x1 n:11I. 8) /(xr= 1-'1

Dtni

se cllM€rplrqHa liAEocHo roqrll{ O; ibysRr{in 3arar6Horo s}rlnsAv.

BiAno?tAb:2.

- Jr^ 6,r,6 UUr.rrr' 3! s, .( -2x 3(x h. t)i ' -5rr6 =o: x B xt2 r 2-'oi r,2 lx' 5r r 6 = 0. l.r I a6o.r. = 6. \Z--\,'-

ltr z.

[r-2=0:

-->Z--2

C*: -2)u[ 1;6]. r'?+3x-. ^ x'?+3x+2(r 3)- ^ x'?+5r 6 - .r:+5x 6 =0; r-3 r 3 l a:u: , 3 ,5r.-6.0. ,.--=-y-}---V--baoox, I,r J{ .

BiAno?iAb:

3a-

l,-s+o;

BiAn@iAb:

ir+s. (3;

[.6t 1l u

+*).

3)rjf 1xr.- 2)\x. 3) 0i(.{-1)(.r

-i\/-='\a-V -3tt

"enapHa

anrEEPA Mep3neKA. r- ra iH. AKaAeMi'{H}ri pigeHb {itliiltii:ii:!:i:

BiAnoqiAb:

:tlliiitiitlii:l

e*:

-6 i

2111 31^,0;

l'=-t' l;r,2, .r 3.

u ( 3; -1) u (2; +-).

AnTEEPA Mep3neK A. r. ra iH. AKa,qeMi,rHran pieenr

flir

367

- 1Xr 3)'< --F\r-=\,,'T\,'+ 13 -2 4) (r + 2)(x

BiAtuosi)b:

l-2',

+ 1Xx

- lxt

3)'=

= -2,

12'

l-='3. L'=

(_ n\ J2. r) t= :, 4 t 3) =.os\ 4) 2 /19'11 tc l9r / n\ tcL -3 | = - tcltt'r = - tc;

558.

2-rf,

r!?ncr

IIepEe piBHsnHs:

,4pyre piBHnrrtrE:

2a247

4x+4V=56

; i-6

. t rl =-srn4n =--: s'nl--] "E

7n /-zr cos-=cost

14)

l-fi rypncr

]l -"\ . -"'3 6, ","4="'"[r" 3 3) -.r"r--. 2' ! a) ="i".-^l

13)

rY, \3).

(.,

n\ -. 23r.-srnlon-4J s,n

15)

560. 1) sin4m" = sin(S60" + 60') = sineO'= 2) cos4050 = coa(360'+ 45o, = cos45" =

tg(

{28 28 7 6' MaeMo ctrcreMy: l;-i

sin I I

I4x+4a=56t

(- n\ 7r E I cos-=cosfzr+t] = cos- =,i

5r! / r nl cre4=ctcl'r cts:= l: 4J =

24/14 xl-24x 14x + "x'1 -"'" pil""""", j4 4 I =0; a;at'l;i-" 1a_,:-i=or . 56 a6o r, = 6, -r2 - 62x r 436 _ s6 Ee 3a.qoBorbHrc n. lr' - e2r 336 = 0, I*, ,.r * 14: * 0, 6x(14 -.jr) x) 0; l6x{14 lr.

Po3B'sxieMo

lpyre

. l.r = oi I lu=6'-

Bidno6idb: 6lrM/roA.; 8 EM/roA

325") =

v3.

l:: 2

-tg315" = ts(180'.2-45)=-tg(-45")=1;

l0' =sin{360' 3. 30")=sin30.. ;i1 te?65" tg(180" 4 + 45') is45" = l;

.l 9,r'

!'MOay 38,qarrl;

' 5J

In . -srnlz'r + fit 4 4)

siLn

rr - '; I "E 4=

""[ 'Sl=-",*'!*- .,u(r"-;J ",";=-f

s61. a)

3. nepioAnqHi OyHKrtii 559.1) sin390"

= sin(360'+ 30) = sin 30 =

2) cos420'=

cos(360'+ 60') = cos60" =

s) 4)

ts 780' = tg(360'.2 + 60') = ts60" = J'i ctg 405' = cte(360 + 45, = cteL,d = 1i

' 39'1 sG36" = f, 6) sin( 390") = -sin(360 + 30) = -sinso" = -l;2 5l

cos{-?50") - cos750'= cosl360" 3

7) !e( 2lo')

te(I80'+ 30')

te30'=

8) ctg225'=

ctg(180" + 45o) = cte45o =

s, cos300'

cos{360"

-*l3

- 60") . cos(-60')

-"oo'= j,

l0) tsl50"tc(180'- 30")= ts(-30') f ' t vb i lln r-zn-= rr / nl =cos-= 1l) cosj-=cosl ^ ^ b \ o./ =cos \ o/

368 llt

AnTEEPA Mep3rrKa. r. ra iH. AKaaeMi'rtrlri piBeHb

iijtit:lil::titi:i

iiltltiiliil{t{r earesPA Mep3nrK A. r. ra iH. A(aaeMi.rHrn pieenu lld

gOg

569. Hexan Mixc

ABoMa cenaMn

l{M, roAi lenocrreAucr Aorae qro Bi{craE} sa

rpaRrop *

*o. Benocsnearcry trorpi6Eo sa 1 roAr{ny 6irBue. -a r 5r-3r . 60 rvracMo prBHssHq: -: 2x 60: r 30. ti. 6=1, 60

BianBiAb: 30 kM.

4. BracrlBocri i rpaoiK]a OyHKqit y = sin x i y= cos x

af-l;-rl; t 2 )

r=-"f-*l' \ 2) r=o s* ,E *.l." -lsn. ,E uz cos4:; 2t ". Bt-t 2.i 2

szo.rl

serpaBrr.rl'o, roqriaA

H€ Ha,',e)(,rrr,

rpa4ix]:

rpa0lry;

3\C( T) = f(x\, ro

'1:)

AoBFAcHo-

repio,q OyH$qii

f(r + T\ = cts n(' + 3) = cte(nr +

3) l(r.) = cte 'rir; 2r: 4) fi.rl = sint5r (t

sin s r-ll

/lx-r)

37t) =

l(r).

\ \

zl sin(5ir-2r4,rl sin6.r

ctg

n'.

1): 1=cos(-4n); 1=cos4r!;-1 =1

Lnr

.'"

', , -".,

B Ha-1F){,r6

HenpaBrnbFo, roqfta C Ee

Ha,,re

,{rrrL rpaabi$y;

= f(x ".o."'9I="o.lrn rr rrrr cosx: "/r'.rr Aou.q"no. 4 4) 4 4 \ 'n)="o"'. 2) f(r) = te lxi ( ---: 2n\ - Iel3.y 2n) = Lsl2r 3,rl = - ts{ 3x\ tg3x. /{r. + It tg3|x ]

563. flItqo f(r +

., ;j,

11 1 n] 1 r r I -[ltn :dt \ D\ =cosl4r--]: =cosBt ,=r; ro.rfta, sane?I{I,rb B

,rr.,, o(t l,2

rpaoiRy.

r=.r:roq,.aA Hanc,,*nrb rpa{i*): \, ll, 2) ) -r "r"l 1\: 1 tr: 1 roqlla B Ee Hane}rlrr6 rpaoiKv; 21 2 =sin2 -=1 2 1); -1 = sin n; 1 = 0 HenpaBrrnbHo, Toqlra C Ee da,re)r ,rrB rpaoixy;

/n 2\ Bl-: \2 3) C(nj n, ,l?!s,

AoBeaeHo'

21. AoBFAcFo.

I 6

r'1,

lJ, -1= -t1(n\rr = srn[4n 2) 2 ","?pa, 6 6), ,=

ro'rKa r] Haie].'rrL

rpaOiKy,

s64. lr /r.rr 2) l(jr +

cos

565. l(:r) =sin

3.r: /{x .,

= cos

3(n

r; l(j' +

566. l(r) = ts jr;

[t.t . rt = tE,! ))

.".3[" -

cos{3ir +

2r) - cos3ir'

572-1) 3n -2n: -n:.0,2n:6n;7n syni

AoBeaeHo.

- t2n, = cos(I2n sr) = cos-3.i. Aose,qeso. sin(t + n)= sin r.; r IIe e abvtlllqii. 'epioaoM

2) Han6in6moro sEaqe'na'$yurcqir

air) = cos(3r

")=

(n ,t,i r,)

.,s*, - I

3) EanMeH'roro 573. 1r Hvni

ucpioaov SvHRuii

567. 1) l(r) = r'? + 2; rpaoilc napa6o;ra, <eirxur EarpsMne{i Bropv, r.oopalrlrarr BeprrnEr (o: 2\; f(r) e [2i +*); 2\ f(x) = rz + 2a='2 + 2x+1 1=(' + 1)'? 1; rpaoin rapa6ona' lBirRIfu nanpsMneHi Bropy, xoopar.rHarrr BeplrI{IIlI

31 11;i=2./r+3;

(-l;

BirRa, lapa6onr, BeptU'Ea

1);

l(r) € [ 1; +-);

Mae ICoopaI'IHar' (o; 3);

<sirna' rapa6on', Bepn'FIa Mae rcoop,lurlarr , 4\ f(r) = 4 3G; z, 568. r) "6.* V7 VF v? {z ,) 1616 Vt - 'S' a V* = 'VF"F lF = .'F VF = s,

l(')

€ [3; +-);

(0; 4); l(,r) €

( -;

41.

37O

i::t:

AIfEEPA Mep3ncKA. f. ra

"r" -+, ;, +, oyEriqis Ea6yBa€ *" Tt -;, +.

dvHk'ii: 5n: qI. r ' 3n. 5n. 2' 2 2' 2 2

7n. 2

2) san6inBuoro sHaqenH.s OynRqin Ha6Fae trpn 0; 8n; 3) EanMeHrroro 3HaqenHs Oylr&qis Ea6yBae npr r; r; 5n. 574. y = sin

575. y = 5in

576. y = s6s 1 577. y = cos

578. rr cos

' VsJt 'i's" 2 {2''=g=, ",:14=e-rc2=:trt V2'

3Haq6EHn

OyHkqii;

Fra6yaae

€ opocralo.rorc IIa trpoMiflr&ax

" "o*t

sra{..

l);

4).

orc sa npoMiniEax 1); 4). Ha rpoMiBrcax 2); 4).

3pocra€ Ha rpoMirriKax 1); 4).

t.6rT .os

r.68,r. o.tsinbHH Ha

]'1,r"l

6u"*o'" "o**.,

2) sin 20" < sin 2l', ocEir6(s Ha [0; 90'] y = si1r rr..r... 3) cos 20 > cos 21", ocdrbtiu Ha [0; 90"] y = c6s r..rr^... iH.

AKaaeMi,{Htn pieeHs

iii:ilil:ilii::::i

:::l::all::il::ri:! AIIEEPA Mep3neK A. f. ra iH. A(aAeMi.rHri piBeHb

::it

371

l0't > srn 25r oc}(r,lbr{H Ha I 3nI , 18 lfii.2 I tor <cos 25n ocxrnbxn f,a I 3nl 5) cos-9 t8, itr: 2 I

4) s,nl-

y = srn .r cnaaac;

y = cos

D-/

y=stnlx+il-2;

ysns Ea 2.

3pocrac;

6) cos 5,1 > cos 5, ocKinExn Ea [4,71;6,28] y = c6s 130o"t""' 7) sin 2 > sin 2,1, ocKinbxr Ea [1,57; 3,14] y = sin t cra{ee. 579. 1)

n 4n lnl cos;>coE;:, ocftinbl(r Ha 0r ; l

y = cos

cna,qa€;

5r!>$n 1711 ln I y=s)nrcna4ae: ocxl.nbKH 3a I Id-, Ltitrl ( zft\ l' an) 3'l 7n oct(r4hlcn as I r, ol >s'n[-loj: -$n30 > srn16, rr) s,nl so.J 12l

,\ u=-;*",,-i).

Y=sintspocra€;

locniAoBnicrB ro6y,qoBr-r:

z) sin

lon

4) cos

l1n ocEtnbKr Ha i tr; 3nl

Z->cos

,, = cos

3pocra€.

580, 1) Ha npoMirrc&y ll,57i 4,711y = sin .' cnaAse; sin 4; sin 3,6; sin 3,2; sin 2,4i 3in 1,8; 2) sa npoMirGy [3,14; 6,28] y = cos

spocrae; cos 3,5; cos 4,2; cos 4,8j cos 5,6;

,.,

*"['-*,),

trpaBop]n{ sa

, , = - i -"(, t),

crncxas',

6' ao

y 2 parr,.

co3 6,1.

581. 1) Ha rpoMbracy I-1,57:' 1,571 a = sin x 3pocrae; sin 1,5; sin 1: sin 0,9; sir 0'2; sin (-0,2); 0,1; cos 1,4; cos 1,8i cos 2,4; co8 3,1. 2) Ea IIpor.blCICy [o; 3,14] y = c6u

"o*""'

"os

582. 1) sin l23o sin 132' > 0, Ha npoMir{rRy [90'; 180"] y = sin 'r cna4a.i 2) cos 4,2 - cos 3,4 > 0' Ea rpoMitrKy [3,14; 4,?11 y = cos t 3pocrae'

51gl'49 co" -" 3 t o, sa apoMixKy loi trl y = cos r

crarae.

sez.

583. 1) sin 190" sin 191'> 0, sa npoMirtliy [181'; 270'l y = sin r cra{ae; 2) cos 1300 - cos 110" < 0, Ea lpoMixrcy [90"; 180'] y = s6s .t saags..

sin cr =

,.,

nocrdsossicrr noey,losa:

"t'('-;), op"uopw "u f ; 3. y = -B "t"[" -;), poarsr ysaoBxc oci oy.

584. 1) sin 58" > cos 58'; 2) sin 18" < cos 18"; 3) cos 80' < sin 70'.

585, 1) cos (r = 2 sin 25'; sin 25"

t) , = -3"r,'(r - 1).

O,42i 2 sin 25" =

JtcosSs'; cos35'- 0,82;

0,84;0'84 € [-1; U; piBEicrb

.,6cos35" = 1,16; 1,16 e [-1; 11, pistticrb

/-\

546- l ) , = sin l x + : l - 2. '

6.)

zt r=-"("*1)

nocmnoBHicrr, tro6yAoB[:

1 Y=sinr; t'nlr. + z. y = ernl,r 6Jr

372 ill:

-r.

rroc,riaoB'icr' no6yaos,n:

1. Y=cosr; nrBop!.r Ha

AITEEPA Mep3rrK A. r. ya iH.

A€aeMirBri

piBeHb

ii'::i'iiiili::i:.:i

*"1'.

X),,riuoow',u {; ::i!i:iil:ii{lil ArrEEpA Mep3rrKA. r. ra

iH.

AKaaeMieHrr piseHb irl:

373

r_"."(,*l]=r. *u" ,," r. s) y =,6""-;

_r-...--;

D(g):cosr_l>0. cos.r a

I: r

,- n EZ= -^4.

; I

588.tr,,-/r->rz , _ , vsrn x, : Dtg): y,6. sin

r..

[2^n; n + 2nn], n e Z; g

sin t.

#ffi

a) 6)

,r.

r'1:

,{J)i,er

-,:': -. o:0,,,, =_",1 I lill,i;::i:,, "t

'"' r - srn "r = 0 seg'

D(v): B; v = c.s

I;;;:;:i:::

a)cosr>O.,,_" 6icosI-0'-'.osr:

+ cos irr.

t) v - (.["",-)'; D(r): cos r ]

0; y = qos .r.

2) 6)

Dlg); -sin" > n. __ -",^=nn,

,(y)j -cos,i:0i

37a

i_l:,:,

artaa""o Mep3aqK A. r. ra iH. AKaAeMieHrr,

piEe,rb

'=Iroo'n.2,

liiji:iii:_::l_i::iiji

375

j/ =

Gin'-;

b) y=bgql; a) 6)

r(v):

D@):

sin,-

A) y-",=

1>0; sint>1; r=f,+2nn'nez;

cost+o; x+f,+nn,nez;

npri

t=-?1+2nn,neZ;

3) y=sin2r; D(u\ a) t(y): [-1;1];

cost>0;Y=1; cost<0;U=-1

y-t,

= 1rp4 t=-!+2nn,neZ.

.n x=n,neLi o, nym QyExqr: 1,. (n l 'clnr;';-nn)-n-zt a-o,sttl'o x.l,- + ftni n +,rn ). n ezi f--l rt y 3pocrac. -- -+-rr," 4 nn,nczi g cral\ac, L4 ,.1f,*nn i{^rn).,.r,

y .0, srqo

)

590.

1)y=sint+ l;D(ulxe

a\ E(yr: lo; 2\l

6) syni OyEriqii: x = -! +2nn, n eZ:

9... =

'.1f,*n,!*nnl,n.z; 1

rpn

t=!+nn,neZ;

V.,"=-1 upn

!+nn,oez.

tn :n-l Bt s ot x Fl-!;- 2ftni; ' 2nn )' n e zl rf y spocrac. rxeo rcl |,znn:|tznnf.ne z: u cn*a.-' """{" A)

*'l;

znn:

!r'

+ znn

n e L;

y.",=2 npn t=!+2nn'neZ;

'=0rur

x=-L+2nn'neZ; 4r

u = -f sin,r: Dtutt x e' R: '2

t,,,, [ !,1l' t=nn,neZi r â&#x201A;Ź (-n + 2firy

6) Hyni Oytrxqii: B) y > 0, s&rqo

2Mt), n e Z; A < 0, aRt\o I

t e (2r1ry jt + 2nn), n e Z;

r, , ipocrac. xel':"znn:'" tzrnl.ncZ: g anaaac,

,, r="'"[,-l),

D(y),re

f l xel :+2nn:L+2nn),nez:

a) t(u): [-1;1];

v*-!

npu

x=-I+2nn,nez;

v-,,, =

-t

wu r=|+znn,nez.

6) Hyri OYnKuii:

'=f,'"'''-z' e(!+ z^,;! +znl, n.zt I < o; 'ce( "'tv'o; x

| * zn':f,* zn')' " 'z; r) y spocrae, snrqo '.l-f,* znn;! * zn')' ''z; v " t '' ***. , . f 1! * znn; -It znnf' "2;

376

piBet" iril AITEEPA Mep3neK A. r" ra iH' AKaaeMiqHnr

illilt'i:il'tiili

i:liilli:iill{ii: UTeSPA Mep3ncKA. r. ra

iH. AKaaeMi.{Hr,rr

pieexs

i{:J

977

1 591.

1) r/ = cos

.:r

1; D(y, x e R:

4\a=3cosx;D(a\tceR.

\ "'\'/ a) x(y):

,[, 1

2;01;

y<0,sriqot€ (2nnr 27t + znn)' ne Zi r) y 3pocra€ rpr r. € [-n + 2fi,zfin'l' n € Z; ycnaaae' mflqojr B)

A)y,,,,,,=0npta,=2fin'n'z;a,,,\= zr "u = cosi\ x-l'];:1) Dru;:, -R.

2 npi x =

\'/ €

l2nni n + 2nn7,

+ 2nn' n e z'

[

t(v):

HyniflHxuii:, -;,",.

') y

3; 3];

o. ex,xo

x.\-'r -znn:')'r,,)., -z: v

z"^,"r' z*,)., -2, ',.." r) y 3pocra€, x e I n + 2nn; 2nnl, n e Zi y cnaAae, r € t2nni n + 2nnl, A) y.",=3, t = hn, n E Z; C,,,",= 3,r=n+2nn,ne Z.

$$,ffi

".1;

5s2. a) E(y): [-1; 1];

",.*. r)

snrqo,.( I r """'i*2",), z, znn\.n. znn,,! -[i

ez;

/ n) yniBoHa br y=slnlza+-J.

a < o,

o r=r"*(r"-f).

y spocrae,

nl r, -o,,,,*- n. "u 2ain(zx " 3t |

nocniAoBHicrE ro6yAoBr.r: a) !, sin 2.ri

6) syri OyEkIIii: x=f,+2nn,neZ; B) y > 0.

n e z;

po3rsr y3Ao',,. oci

.r r=zs"(z'.lJ -L

'.1-! *z^,, !*zn)'".2; v." t",

yri,,s sa

oyy

2 pa3r;

r oatrE,rr'.

'.1l3\ * 2n,,4ri n zrnl,I n. z', r)

v.", =

t, r= -\

+2nn, n eZ;

= 1-

1 = !l\ 12nn.

r .7.

zt y=""'|, DQrxeR.

(, -\

se3. y=-3sir,l;a) ,s(y): I 1; 1l; 6) Hvni Oysftqii: t=fi+znn, ne Z: B) y > 0, sl{qo r € ( 7L'r 4nn1 T + 4nnr, n e Zt Y < 0' FKUro r .- (n' 4fn. 3n - 4rnr- n I zi r) y3pocrae,t€ | 2n+ 4nni 41Lnl, ne Zi v cnaAae,:r € f4nnr 2n + 4nnl' A) y.", = 1, r = 4nn, n e z: v,,,u, = -I,r= 2n+ 1nn, n ' z'

378

6) 2t Dtsttx-

IIocniAoBnicr6 no6yAoBr:

ar Y=sln_

:;:::;::::::::::::l:::ai:l li::: AITEEPA Mep3nel< A. f. ra iH. AKaaeMi'{Hlri piBeHh

(, rl - , srnul " \2 6) " "

n 6

:::!iii:::iiirti* AIrEEPA Mep3nrK A. f. ra

iH. AKaaeMi.{Hxn piEeHb

lii:

379

Ma€Mo crrcreMy piBIIsEb: 3)

, = *""(; , = *",'li

-i)

l+x *_"^ '"'

posrnr ysaoBx{ oci orl v 3 pa3r';

-;),

, 2. yropy Ha 2 oA{'sqi.

t;=ro'

= 6Oy,

oo-15 6o' = ro.

i: -___- = t0; lx l5r u+ lu 15u+2 " -15 1

l5a +2

PosB's*ieMo Apyre piBEsHIIs: 60(16A t2l-9O0s 900y.120-900y-150y-20

,^'*

tbvl

roo

0. 1,,' _ 150 t..1'_?" n. ts' .2 / o: ' Io"-r5r Ly+-1b:

1s0e

100

^ -150y-100=u:^ =u: -u+2

1br+, a0' l.r =

Ir-|

BiAno1iAb: 40 *M.

5. BnacrraBocii i rpaoiKn OyHKqifi y 594. 1) l(x) =

:-x'-3x+2 . ;

r'z-3x+2 --=u; - [x'at+z=o, lir-1+01

l(x) = o; -'-

BiAno,iAb:2.

Z\ f(x\ -,"[x'zli,

ocrcingftg .r2

+9>0

trpllr€ B' ro Ovgrcqis

EvniB He Mae'

BidroBidbi Ee icHylorb.

x',lii; D(y):r-1>ojr>1.

f(xl = 0; xJt

I=o; x=oa6o.:=1; t

= 0 He saaoso,'lbHn€ D(y)'

Bidnoeidb:1.

-2t Dtattlxl- 2,0: lxl> 2: r c l -: -21\- l2i +-)' = ot lx 2 = o;lrl= 2; x = -2 ^60 x= 2

4) Itx,=

,!i'l i

J-lx

Bidnosidb: 2i 2.

1032t _: 2',.10" 10= 5

=\zl

/-\/-\

Bl-;'-Js]t

ctg x

1; Eenpasrnb*o,

=\21

-ft =tc[-;],

rpeoi$y OyHHqiii 3) C (tr; 0); 0 = tg

ro,,*al

,,e Ea'e*c'rb rpaabiriy

= Jt,

EpaBr{nElro, ro.r&a

B rlanes.'rE

0 = 0, npaannrso, ro.{xa C Ha,re)rcr.rrr, rpaoiEy Oylrxqii;

roqRa

HanerltnrE

rpaoi(y OyErcqii.

598.u=ctg,

l) Al^:l]r z1

1=crc;: 1= \

r] {;ol;

o=ctgl

1, npa!nr!,'ro, rosxaA Eanex'{rh rpaoiky o}'Entrii;

/.-,

}];

nqii;

-^fc[-u;fJr It '6 'v5) t=""[

0 = 0, rpaBunLso, ro..&a B Hsne}crrb rpa@iIcy O}'s-

rnr

a'J,

rpaoixy Q]'Ercqii;

= 21.

-.,6

, , '!l -3G Jj ,, "[z'. Ja). Ja -,-zt. - Ja=te['I-6J; o,'[u,t,-B=tc;' l T."*"',"".

/o-

3\a

uru.r,It',"|=,il3"/ \2,.r0) lziJ .ro. !\s I"i ,ili r. .3{/ uri tJ zt -r:u] \3'?',

r-ru(-;)'

tg x i y

4yHrcqii;

Jx=1a6ox=2,

s\ f(r\=

5g7.a=tgt tl "(-;,t)'

*r*,

'.,4), , He"(f; lr8lrexinrb rpsoiky

!e=-n6, "E =

"t*[^

O}.IrRqii.

uenpaauarso, roqna

iJ,,6

-f

lr€ Ira,r$$&rr,

""nn",""r.8o.

roq&a

3n, 5n, 599. 1l Hv,rsMu dvgftrii u = crs -r c 1, -I, 2' 2' 2' 2) ne ra.rexarr o6.nacri BlraIIa.reHEs ibyr]Iirliii O: '1t;2it. 600. 1) HynsMs Oysxqii y = tg

'60"15

380

:.iil AITEEPA

Mep3rt( A. r. ra iH' AKaaeMiqHnr pieerr {ill{ll:i{:}}ilt

n; 0; 3n;

He ua,relxa rE o6,racri Brl3ua,rcHnr

:iiitli:iit:jll::i AITEEPA MepsIeKA.

tX r: -Tt -X, |, r. ra iH. AKaAeMieH r piaexr l{! ger

Oysxrii

60 l . 1) Ha KoErsoMy 3 rpoMir{tldB

y = ig

3pocra€' or}ce,

606. 1) y = -ctg r, crMerpis y = cts BiAHocEo oci Or.

2') v = cls r + l, rapanerrr{e nepeHeceHIIn BHu3 sa 1 oArnlrq&.

38") > te(-42");

tg( 2)

l!*n*,!*n).*.2 \, 2 )

2n< tg-, 7n tg-.

tg 130" < tg 150';

5) ig 1 < ts 1'5; 4) tg 0,9'r < ts 1,2n; 6) Ha lior*{HoMy 3 rpoMiJ{KiB (rk; tr + fift ), & E Z v = cig n cnaAae' or]rle' ctg 24" > ctg 28'; r 3r! 8) cte ( a0") < cts (-60"); 7) ctcT - cts?: 10) cts 2 > cts 3.

9) ctg 0,4r < ctg 1,4r;

u=te' ( !*"u,|*^n)'o'7' o-}t(F: clg claAac rh, P - Z 4 'r

602. Ha (oxcsoMy 3 npoMi,rcxiB npovixKrB lnftl

HoMv J

1) tg

0,?); cig

ndpa,rpnLsp nppFHecFtsFF

Br iBn tsA

6) cte (-3) < tg (-3,1).

1,2);

ts(

O,4\t 2) cts 3'2; ctg4'6; ctg 5'3; ctg6'

te 1,6; tg 2,5; tg 3,6; tg 4'1i

(

-].

3JI> ctg 5n -:

603. 1)ts1,2;ts0,9; ts0,5; 2) cte

.r +

4) ctet

3) tg-

604.

(

3) y . rtcl

2) cts 100" < ctg 92";

110" > te 90";

2n< tg 5n -; 5) ts (-1) > tg (

3pocrae' Ha t{oxi'

(

1,4); cts

(

2'4); ctg

605. 1), = tg t' clrMerpis rpaoiria y = tg :i] BiAEocso oci Oir'

(

2'8)'

2) EE

=tc t + 2, n^PanenEse repaEecei' lrroBEt oci Ov IIa 2 oAIrHErrl Bropv.

u=te'+zl

celinn

n1 s =

"tc|,,

po:r.sr yonosxr oci O, y 2 pa3u.

4) g = te r, crlzc( YsaoBri{ oci O, y 3 pa3lr. pa3lr. I

*(' - ;), napanerr.senepe'e' y = tg r BnpaBo Ea t.

607. l)sino

99 -ts80"-3.78:3.78a I li lli ;1980':

piBHicl6 /p vo}t{nuBd:

21 costt= ctg!; "18 ctg+ -tA - cts10'= 5,67; 5,67 e l-It 1l; piBHicrb IIe

:r coso rgf "q : 1gtr "q = tg20'" 0.36:0.36 - L r: Ilr

Moxnr.rBa;

pisHicrb vor(,lrBa.

608. 1) sin 78" < tg 78', ocrrinbKn sin 78' < 1; tg 78" > 1; 2) sin 40" < ctg 20', ocl{inbK]I sin 40' < 1; cte 20'> 1.

382

i:::::

anfEEPA Mep3ncK A. f. ra

iH.

Al(aaeMi'{H}ri piBeHb

:::::::::i:::a::::::::::::::

::::i:ii::l{iil::i: AnrEEPA Mep3ncK A. f. ra iH. AKaAeMi.rHrar pirenr

liilt

383

ooe.

*c(,

6) y=ctgl,rr -], Br

zr ",="t"[s' "\

1. rlocniaoBriicrb ro6vaoBll:

Il. t2)

IJocniAoBHicrE no6yAoBr-r:

^, a=ctgt:/n)It

ctclx -

;].

$aparFnbHe nepeseceHHfl BnrBo Ha

t, r.ear-*"

""penecelrHn

a) !-cteI' 6) y - ctg 3r, crucx yeqosx

ociOrygpasn;

/ _\ st "z=ctsl -\ sr l:l

Bropv Ha I

12)

naparlenbse nepeEecerrEf Brlp3ro Ee

r. ry

y = (ur"te")'

lx*nn,neZ. L- ut:1 " lctg

2 0;

g=ctgr.

2l n a) 6) B)

"Ls 2x-!.

g=tg,;i U Lg 2x..'tvc!r u lgl2x ^ I,

BflpaBo

61o.

nocnjaoBHicrb no6yAoBr.r:

v=tsx+telrl Dtut: x+I+nn-nez: a) r>o;y=2text 2t

y3rcs}l{ oci

Y 2 Pa3x;

napaienbse nepeFeceHE{

x',oty=O.

ft Ha t

( 2rcl.r'';27t.rJ.

a, a =te

.-i flocniaosHicrb no6vaoBx:

'i / 2nl 6) v=2â&#x201A;Źl.r+;'J, napaie"lb'e nepcHec.IrH' sriBo Ha / 2n\ Br s 2tslx'?J. n*'* v"o.'* oci ou v 2 pas'l'

+!+nn.,ez. 2 y=nk,hez.

s1 y = .!,ts";; o1yy.

zfi

{: tg'z * > o; ,1 L: 2l

ctsxl

)x*n+nn nez, ^ur. lctg r * 0: a) y=l,nllqoctgr>0j 6) y = -1, snqo cts: < 0.

384 ii:i AITEEPA

MepartK A. r, ra iH. AxaaeMiqHnr piBeHb :!:lli::::::i::ii:il

;:i!:iiflifiltli

AITEEPA Mep3ncKA. r. ra iH. AxaaeMieHr.rr piBeHb

ll,

385

T 6)

s) a="te* J.tc.";; D(g):r+n+nn,neZ. y = cte )e - lcte xl a) ctgir>0,y=0;

= te x.

D(y\:

erqe oci Or Or crMerpis -

(;."",".',")

fpaoircoM OyHRrrii € MHoxclllia roqox is xoopA EaraM

!+t+nn,neL. 6e3 3Mislr, Elrxtqe oci BiAEocEo oci Ox.

. 1J 1t

rsr a=Li'"' u ts r'

po3r.lsHeMo

,x-F--nn,n.L, l-,12z "n'n' ' I1*' | 2 "^,,.t,'' otl,

0, o,

ltg,. -

te' > 0.,.(."u,

"o,

"^. ^ u. t).

..2' z' a=

rpaoi]{oM e rp.aMa, napanerbHa oci Or.

p*rr'n€Mo tg

612. 106 no6yAyBarr rpaoiK 6vHKqii, Eeo6>riaHo: l. 3Haiire o6na.rb BrirHaqFlrHt OvHXqii: 2. BlrKosarr'I Heo6xiAEi reperBopeEHn' po3Kplrrlr MoAynb' spaxoBvrotrt rpoMr'{rfttl' IIa sr$rx niAMoAyrl]'lrn ii Bt'Ipa3 Ea6yBae AoAarErx ra BiA'€Msux 3HaqeEL

< o.

ffi'

''"!,,.2. z t.

xe(!+nn;n+nn,u.t). ,= J81, o=-t,

rpaQikoM € npsMa, xaparerLEa oci Or.

L nnl'n-Z lr q (Jre*l i 1sx--oiDtat: nn::' 2)

u=te*+\Ec\:

Pogi'nrHcMo tg

.ir

2, a = cte r

ctg lrl;

,(y):

jc +

+ lte rl.

- 0. .r -ln^r\t^r,^.71. LzJ

fpaoilloM OyExrtii Pos!,lslreMo

D(a\ = R. a = rg

€ raEreEcoiAa,

.(! t

po3rsrHyra

nnt n

* n,, o .

u Lex I re:tiu

2tsx.

B3AoBrrc

oci Oy y ABa paslr.

z).

tsr - tc ,;

v = o.

fpaoir{oM rbyH(qii € npsMa, sl{a B6iraerEcs 3 Biccrc Ojr.

nn, n e Z.

= ctg ir cte x; a = O. IpaOiI.oM rDyHRqii;a npoMir{Clv r. € [O; +*) e rpsMa, slia 36iraerEcs 3 Bicclo O'' p.""""""..'t < o. v=ctg* ctg( x)i a=ctgx+ ctg t; y= 2 ctgt fpaoiKoM po3rsrHvra $AoBtrc oci Ov OyHl{qii Ha .tpo*i*"v t l (--; 0) € noraHrellcoiAa, Po3rnsseMo ir > 0.

6ry

ictgrir Dtyt:!

' nn.n-2.

Cro.rarKy 6yAy€Mo rpaoiK OyHKqii y = tg n. t{acrnlry ryaoixa, slca 3Haxoalrrscs sx*{.{e liA oci Or, lino6par{a€Mo cnMerprqHo oci Or.

[.te\;

-ctg'x

> 0 Bllnoiiv€rEcg 3a vMoBIr, rqo

! Dl!:)'nn.n-7t r^2'2'2 ^^., -z: 386

:;:::::

AnrEEPA Mep3neK A.

npu

ctg't

= 0'

x L nn'n-7t a'o'

ra iH. AKaaeMi'{Hhi piBeHb

:a:::j::::::::::::::::::::::

:::::i!iii::iitli: AIrEEPA Mep3nqKA. r. ra iH. AKaAeMiqHrt

lt*

piBeHh

l!,1

347

r 613. Hexafi a, = -4;

a,=5.a,=o,+6d;-4+6d=5',6d =9; d=

1'5;

614. Hexafi

.l q'=

256,

BiAnoqiAb:

= 256: bi= 1. bi=

qr=- 1- aoo q,=

_Cl

.qa;256.4=1t

l-it podirflnl!

2-i po6irl

3 lq3

4' 4 I) 64:. 15, 4i 6164: 16;4.

615.

3) ctg'

IIpoa]'rirnBtricrE

Itirbrcicrb sacy

Ha 3 Aerani

na 1 aeH;

6inEme

ItirrbLcicrB

aeranei 90 Aeraneii

---1

90 Aeranen

Hexaii Apyrdi po6itEr'Iri Br{roroBnsB x Aeratefi

90=

3a AeEE, a

ra aegb. ncpu{fi po6irnrR rpaurcBasr + 3 .*"i". u npa(loBaB sa I nesb Me$u,e.

trepEtIi

apv,,ii -

9:0

+ 3)

Aerui

a"it n"pt";

_ 90 - r. 90 9.L I O, 90x . 270 90x - x' 3-r O. (rr3) a xt} -' x x+3 {-l} x'-3x t27o n. f-r-s'.270=o. x) Bx 2ro=0.,D bt-4oci r.(.r - 3l lr.{.r + 3l 7 0i D=g-4' 1 (-270)-1089; , - = 33: x. = t-38 = 18. I'e 3a.ooBonblnc vMoBv 3a4aqi: x,' 3,33 -15' JD z ;;-;" 90

15 aerarefi qoAHF BuroroBnsB Apyrnii po6irl{rK, 15 + 3 = 18 Aera"'rei BnroroBnsB

neplllHii po6irFsk. BiAnosi)b: l8: 15.

6. OcHoEHi cniBBiAHotxeHHn Mix rpnroHoMerp[qHrMn OyHKqicMx oaHoro r Toro caMoro apryMeHTa

iin'o:

2) (1 - sin'2cr) = cos'? (1; 3) 1+1=2; 4)1 (sin'34 ' cos' 34)r I l=0: st "o"3 og'c, .os.i sind 6l= srn d 1 coso 7) 1g' di . cos'a sin" d lcos g zcos (,; al .os'd r sin'.l I =cos-d / 1 ,) " sr -"'o .i, cre aJ ' cos'c-r {l-ros7cr)- -sin7.r;

[

!e#=r ro) 'i":q cos" F $n' p "x ' 11) 1' sin't = 1 sin'- = cos12) sin'zo + 2 sin d'cos s + cosr o + sin'z& - 2 sin d cos cr + cos'z= =2 sit\" d+ 2 coE2 ct= 2(sin'c, + cos'?d) = 2 1= 2.

388 lrj

AIrEEPA Mep3nrK A. r. ra iH. AKaaeMiqHni piBeHb i::itiiiiiiiii{::i

sin'o) - cos'crtlI -(tctg'c+l= _ ----;----:+l=sin" c sin? cr' -(l - cos 0, i sincr cos cr L':| / cosc sin a \' :ra.::_:, 5) :ii:.' . \ cos.r I / \sinfl 1 I =sin.o rcosru =1; sin Cr sin' (I sin) n sin/ a 1-ctg?d{l-cos':o) - cos'c sin':c I cos)o sin'a " 'sinc I ?) -+ - ts'20 = 1; 8) ts, p + 21g P.cts B + cts,P- (te,0 2 te p.crs B + ctg, B) = = Lc'1 9 + 2 + ctc, B - tc, F + 2 - cte, F = 4, 4)

ore. rr

616. lr

I+cts'5d=--: ; srn- 5ar

617. 1)

e,= -2,5i at- -l' a1= 0'5t tt|= 2i a6= 3'5. BiAnoqiqb: 2,5t -1; 0,5; 2; 3,5

I | ,13--!, -l - vr3 4 ) 16 16 16

lll '4'

t4 16

, t.

He BrzrioHyerlc.fl ocHoBHa Tp{roHoMerprrriHa rorollEicrr, sin2 lx + cos, (r = 1. Orse, piBllocri oAHoqacEo Br(onyBarncs IIe MolcyrL. 2) 2,5 - 0,6 I ,5; 1,5 1. ' He BrrftoEyerBcs ocHoBEa rprronoMerpaqHa rorox{EicrE tgs. ctg (1 = 1. Orx{e, pi4nocri orllo.racHo Br.rKorryBarscs He Moniyrb.

6te. r)

l2l',131'=1*-s -13, 13,r. \5,/ !5,/ 25 25 25 25

PiDHocri Btrt olryBerscs se Mor*{yrb (arB,

1 45 5 5 +l 2l -4 7-= s 4 94I I

no.ncHeHH.s Ao saBAsEHn

N! 618 (1)).

PiBsocri Br.rKosyDarrrcs He Moriyrr, (ArB. roscHerrl1n Ao

aaBAanH.tr

620, PiBEocri BfinoHJ,.BarIIcs se Moxcyrr,, ocKinr,trlr sin, d + cos: 621. 1) 'firiqo tg dl > 1, ctg ol > 1, ro tg s ctg cr > 1 2) filrnro lts dl < 1, lcts cd < 1, ro tg c.. ctg o < 1. Ane tg o ctg q = 1. OrBe, HaBeAeHi yMoBr.t Blrr{oHtBarrcs

Ni 618 (2)).

= 1.

He Mo)r{yrb.

J-, ll I 2rgq . Lg'a' I -2tgo r tg'n = -J- . l" cos'Ct cos'd cos'ar

622.

sin'? c, . cos' o + (cos, s), = (sin, d + cos, ci), = 1, = 1. sincr(1-cos) + sin c[(l + cos) , sins sinocosc[+ sinc{+sinctcosd _

2) (sin? s)' + 2

3)' =

2 sin

(1+

cos)(l

c[)

cos'

"i;t; "i" "; r\ cos0 sin0 '' .ino-f*"o"o cosd+l =

cos

cosoll rcosl .sindsinc 1

"lnaft*.o"f

"i""O "."a "t"; iiilll:*l:liii;.1AITEEPA Mep3rqKA. r. ra

coad+cos-0+srn'ct sin (x(1+ cos

iH. AxaaeMiqH.,rt piBeHb

,al:! 389

il + sin cr) cos'zcr' cos cr(1 + sin q)

(1- sinoxl

1- sin'

cos" cr

cos a(1 + sin&)

1- (sin'+ cos'o) cos

s(1+

(1+ tg" o)stg"

I \

7')

a(1+ sina)

cos

-. ' ,

1+ 1+ 2cosc

sin'+ 1+ 2cosc, + cosd':

sin'z- (1+ cosa): (1+ cos s)sind

(1+

(1+ cos s) sin (}

cos Cr) sin

2 , 2+2cosa - 2tl+coss) (l fosslsind {l cosa)sind sin0 sins sin P -sinocosp -. cosd cosP sin o cos B + sin 0 cos n . coscrsin0 sinssinP " "*o "o"g """".*0 sin d sin B tsin o.os ll + sin p cos o) sin d srn 0 singjlnll rsorsBr

SHaiLmu: sir. a;

sin'/ ci = 1 -cos'?

,rr;-**....-= "

cos rr cosd.srn(I cosa) coscr 9) sin a \ cos(l srnc / =-:sln s sino l -.1-+_siny-cosy.rosy siny_ {liny losy)cosy _ctgyi 1or --' _jiny srnf {srnY-cosYr cosY sinY 1 sin'y 11) cos'zd(cos'9s 1) + sint cr = -cosz .t(1 - cos2 c[) + sin2 s = cos2 o sin' d + sin" ft = = sin' ct(1 cos' o) = sin: cr sint a = sin{ ct; 12) sin'd(sin' o + cos: c{) + cos' c{ = sin'9 s ' 1 + cos' d = 1; t3r cosct-coso ig o cos.r{l ts? ct, "'i* aj.* = 1 - l- sino sin0 1-sinp+sinP ""1r, tclr 14) r sinB .,=0 *"p p cos

-"F

"".0

623.

l) r 2cqll-cte,9-1 2ctsp cts ll","t

2, sinzd cosr,rtts s

= tg(x,

624- 1t '2 IInHn: adsa = .

s.os ll{cos o sin p I sin Gcosp) .osocosp taSa (1 ctg':3s) tgSq ctg30

ffio /sina

","t

sin'z

sinf,

Ein

x(l

si n

r.)

r. i I sin r --.-_ cosr.(l - sin x) 1 1+ sin,

cos cos

r(1+

sinJr)

r(1+ sin

cos'p- I 2sinp I sin'p _ 1+1 2sinp _ p:rgrp:lr n p) -1414--9 ", "." (1 - sin P) cos B "' 11 sin0lcoso ( t - sin o)cos P 2 2(l-sinpr 2-2sin0 -_(1 P)cos P - G sin P) cosB cos P ' "lr'

iH. aKaaeMi'{Hr4i

rscr=.,6r

"6. 3'

"igc=f.

SH,aLmu: cos ct;

lg s; ctg s,

, "o"o=t.,[ "irfo; "o"o=-',/i-O,6" 0-6 3 4 r tso "0-84'33 : cts(l - - 1-3') ,qaHo:

- SHanmu:

Ryr

II qBepri;

cos

tr=

0,8;

3rr

te a =

si[

octrinbrr]r

&; cos

d; ctg.q.

./5

$ noxo: ate..=-! i !4<a.:". SHaiLmu: tg qi sin st cos a. p,s t'o t'o = q = !. 'cta0'4 'raHHs:

cos r.

39o . ii*: AJTrEEPA MepsrqKA. r. ra

-.odo, "'"t -r[l tgc'=-!5. *eo=*o!,

tr. o.n. 2J AaHo: sino 0.6'

cos'p

sinr+sin':c+cos?:r cos

",no =.,,[

$, rr"= +,;, a6osino 6: ,rt=f,!,

2cosF

cr,

cos 0 sin 0 + cos 0 + cos F sin

d.; cLg

"ino=

=sin2n+cos2s=1;

cosF

lI"II r, tg'si cosc/ rr/l "tao E, ,t,s, "o",o ocftinr,&r cr Kyr III .rBepri; *""=-,F=

p="r,i"p'

rl+crg'd+1) "t" " """'1J,"-;"',")

^. cosB(1- sinP) + cosP(l+ sin B) r' -- li+ sinBxl_"'nBJ

(cos.x + sincr)sin s _ cos q(sin o + coso)

8) cos'z d(cos'z d + sin': s) - cos, 0 - 1 = cos, d . 1 - cos, Cr - I = 1: 9) sinz d + cos'zcr(sin? cr + cos, c.) =sin'9C[+cos'cl.1=1; 10) tg c . cte & + sin? cr = -1 + sir' cr = -(1 - siD' cr) = cos'zd.

cos

^. sr

1 sin': a 1 c[ ctg'c, + 1 cos'9c[ ' /- sincrl cosa+sina -=-=tg"cl; . sind + coscl "'"cr) \ cosc/ coso/ coscr

tg'q(1+clg'?0) _ te'a+1 -

sind)

piBetr i:.:ililillliili:j

= 1+ ctg!

o; sino=t

"itf " ocRi,'l6rair

c[ &yr IV .rBepri.

:tiitttitl::i:lt: AnTEEPA Mep3nqKA. r. ra iH. AKaaeMi,rHr,rn piaexu

.r:l!:

391

q titto sina ,/_' =-L--'!1 | cosa=r'[r sin,c; !50 5;2 1O

""so

uii:1-6py

= 16

- s,a6 = ."f0, el =

625.1\ AoHo: coscl=- i u < d S'ailmu: Ein e; tg 0; ctg cr.

SnaLmu:

"o"s

cos ct.;

1J]_

ocRinbKn

(cosd

' '12=5 13 12' .tno=12 5

&i sin

pess=-

"o"o

= -.'fi

*in

tr a

!10 Jto 4) \aHo:

ctsa=

SHaitmu:

teo

$i sin

-L, c[g 0

E. "r"o = !l+7'

te"

i !<a

ocxinl,x,, c

I -sinocosd

sin'rr{I-rg:o,,t-

:.:.:.:.1

"(0l 1;--- r \l \sm-c )

;;t'- : l

cos'd/

cos'

a ctst a

",";*.i""",

2r sina = I

Ryr I1 'rBepri.

392 iii: AJf |EEPA Mep3neK A, f. ra iH, AKaAeMi,{Hnt

o|t

I t ctg'd)

= co", o

sin'.r - "."r

1) sin'zlI cos'c((sin'ztl

H#--"."

+ cos, (r) = sir, )

n cos,

sin2

= "os,

cclg,

ct =

sin.c cos,

cr . cos? ry

_srn,c ros. o

c, cos, o|;

_ sin'/otl cos'?d) cos"c ,, _ " "' 1"i.lo lcos'c -"r",ol.Ie'g. sin'c sin s";n.o "oa'o _sin'?csin'o cos'a ,. G

sin

coso(l + coso)

t, - 1 .os, q . - |= câ&#x201A;Ź^ \ qin'd

"*,of

ctsuc:

srnotcosd- lt.l

sin,o L / "f_g. "i""a,f""":"__..","J sin'cr I cos, q(l - sin, d)

cos-

piBeHb ::l::::l:::::::i:l::::

4cos, d +

clg d 'Lg'o t cLg'?ol

= tln a.

627.

L=t+cts,q;

sinocosc+sinc -"tnt' "o"o I cosc cosd . sirr' a 1 +.Lg' c( cos' a ::+cos? u = I -.tg,

= cos'

3u4o

i:lid

"#=

4 - 4(sin'? o + cos'? ct) 4 4 = =n. 12cosd lX2sin(l r Je) rZ"o"o l)(2sind + J3) "'

ftit"

@=e"*"_1)12"-;16=

<n.

1= -1,

(coso sinoxl + cos(lsind)

\ ----.- sin'(}=sin'o ^ / I 3) sin'n cos-d \.oc'o l sin':c tg:c: z"i,'o 1+2coss--ll -'-. "6 z-"o-r 2sinc+Js (.,6 -2sino)(JE + 2sins) - (1+ 2coscrx2coso - 1) _ g - 4sins

ct; cos cr.

:.:.;

2) cos'd+sin':s sin'7c+sir'zo!g a=I

1, .tgs=-l r cLEd=-3; srn- cr =1-ctg'oi sincr=tg q t.'-, ocki,rlxx d Kyr tv.IBepri f ",'"= \ I + (-3)' ,,[o

pesynr,rari Mlr oAep,Iianu piBHi Brrpa3rr.

cos"

cos c(.

L 1 srnc = ., \110 JIo

sin'o)

=1a19'q=-l; cos,o

tlct !, !. ".r* (}i

SHai.Lmu: cte

l- sinocosd y

=2.E,

It < ct <

sir\(xxcos'cr + cosC[sina +

t(yr I .rBepri.

a r'iT- Jr a: reo - Ja r ,[5) Ja roscr It-*== -:l n l'ffi= "6, rei t/,u 4 "/1t J33 "6, 3t naHo:

!- loo

trpaBoi qacrfiH ii oAepxarn r0r. 1) BIrItoHaeMo reperBopeHEs niBoi .racrlrEn:

tg ct; ctg &.

"ir,'cr;

7,[2

626, IIlo6 4onecrn roroniEicr6, Eeo6xiAno BnRollaru roro*cEi neperBopeHss olHiei a6o ABox 'racrrjs rt oAepr{arr oAHarioBi B!rpa3r-r. Mon {a cKnacrv piafir.rqrc niBoi ra

t.,/illll'o; "i'o "i,'o f 144 E{ s srntr= Vr -=11*n=ra, 2) AaHo: si,ncr

| lr .12

rol ! L-:'I

,,6i

f ,il coso .j1

srn' .I srn_ rl

llilli;::jilltiii

ATTEEPA Mep3rqKA. r. ra iH. AKaaeMi,{Hur piBeHb

llil

393

cosa o(1 - cosz c[) = sin{ d cos2 Cl + cosl o sin2 o = + sinr cr cose o(sin' o + cos2 c!) = sinz c cosz d; 2) (sin'zd)3 + (cos: o)3 + 3 sin'?c(cosr q = (sin's + cos? dxsin{ c - sin2 o cos2 c! + + cosi c[) + 3 sin! o cos2 C[ = sin! C[ - sin'? q cos'? q + coa{ c, + 3 sin': ct cos': ct = = (sin1 Ct)' + 2 sin' c cos2 cr + (cos1 a)'z = (sin? cr + cosa a)'z = 1'?= 1.

624, 1)sin{cr(1 - sin' o) +

c[ o

2(sin'? o + cos' sxsina sin' o co€'? d + cosa (x) 8(sin! o+cosa d)=2sin'rq sina d 2 sinr Cr cos2 s cosi o= 2 sinz ocos2 cr + 2 cosa 3 sinr d 3 cos{ = -1. = -(sina Ct + 2 sin2 o cos2 ct + cosa q) = -(sin3 d + cos'? (r)' =

629.

(t=

-l!

630. CxoprcraiMocs ocHoBrrom BnacrrBicrro Apo6y: st qo qucer6HxR i BIraMeHHrIx apo6y roairtrrr Ira oalre i re ca e qncno (a6o Blipa3), BiaMisse Eia Eynt, ro 3saqesrrs apo6y Ee 3MiBr.rTEcs.

1) lloAirsMo

ql,rcen6HfiR

cos -cosd_tsu-1 _( ,. -rl,(, * r) ___r, n __t. sind cosd tss-l \3 ,/ \3 ) 3 3 2

631.

cr:

aHaMeBHLtIr Ea cos

_ ^l

D+DIgC 3tgd-7

80 ,25 55 55

2 6 I " 2 " -5,5

2) floainnMo

qncenLHr.rR

"t" " "."

bos o + sin al; "ir "f = roMy q .rBepri, III cos o < 0, sin xyr P$xpr{BaeMo MoAynb: s + sin d)

r,6;"

= .[."' t r"t" a

(I < 0, cos cos

cos s sin p :

u"".

"tno

-cos'a = sind \i"in, o

394

lcyr

"""

cr + sin o < sin c[.

"t"' "

qBepri, sin P > 0; cos

sin ll < 0.

636. sin, d + 2

-1 <

ili:AITEEPA Mep3nrK A. r. ra

cos(r

Cr .

cos

cos d <

o + cosz d) =

cos

ctt,

c! cos2

= \-2.t-glJ-

Cr 2 sin2 q cos'o= (sinz d + l-b1 2b'+\ -l+2b'-b4

cos{

422

cos2 c[ = sin2 Ct + cos, 1; 0 s cos2 c[ < 1; 1 <

= 1 .t cos2 c,: + cos, a < 2; 1 < sin, d + 2

:::li:l

cos? {x

*w,o -

i,i.iil aose

o < 2.

7 -. /(xr) r_,:

BiAroBiAs€ MeEIIIe sHaqesds

7 f(x,) ,,_-5.

AB_ 7(\-x,t

iiitailliii:::'t

2) OyEKrtis 3pocra€, .EKrr{o 6inburoMy apFyMeEry BiaroliAa€ 6inLEe BHa.reHEs OyBnqii. Hexail x|- r,. l(xl)=6x, -x'zt fk,t 6t/-r:. Cxrs{eMo pisnnqrc ssavefi r 6ysrjrii: t6a, x:) - 16x, - xi t = ax, - t:-6x, xi =6(x,-rr) .G:- x:\= = olIT rr) Ix. - xtl(J, + ir.) - (.r, xr)t6 (.r, - ,r,)). .r:-.r, >0i -t, .r, < 6. rovy 6 - (i, , i,t o. ' (,Y? - xrxb - (x? +:,)) . 0 npn.r € (--; 31. ' IQ,l - I(x,l ' 0i t'ta,t . lr,), orxe, OyHKui' rpocrac. *

[#J' t25.

=1i",,]

r"' nr' ="1t'2)=" =/ =1_r \ 1000 i

t'=

\125/

= 126t =

,,[#]'

ctg d < 0.

iH. AxaaeMiqHrai piEeHb

r >I

sl{qo 6inbuoMy apryMerrry

t:.:.i! .:.i:.:{

637.3 sin, o - 2 cos2 d= b sinz 2 sin2 q - 2 cosl c, = b sin, 2(sin, o + cos? o.) = = 5 sin'd - 2; 1<sin ct< 1;0 < sin3 d < 1; 0 < S sin, d< 5; 2 < 5 sin, a_ 2 < ij;

*,,,

|]",Jr,sin,o tl "i,,o-.f,o

\i,

0, roMy

sin

3) sin!c + cos. d=sina d + 2 sin2 2(sin

,(s-b')

7 _ 7

- lcoso.ctg al;

(yr III

a6o IV .rBepri. III.rBepri: cos ct< 0, ctg

axsin,

,,+5 z,+5=1xt-35-7x, (r, +5)(r, +5) (r,+bxr,+b)' 0i ,., + s > 0;.r, r b .0 npx;€ (-s: +-r;1r,1 _ L*,,. Ifla,\- r,.< flx,1, orxe, gyE(qia cnaAae,

!9{. !in d (tgpctga) = -"o"o. cco"F. "inp, sin lJ cosd = "in

r'"+"

= sln a

q < 0;0

cos

CknaAeMo pi3Erqro 3EaqeHB OyHXt-tii:

-*d"*f 0 VGs,c"-lp coscs:npl. ". v6*'"tcg.te" '1[oJ"{l*."'P) "' tep.tc" - tse"te" - tgp.tg"' qBepri, cos - Hyr III Po3Kp{Ba€Mo Moaynb:

.(, ^t'rl \ 2)

1) <DyHAqir craAae, OyHIcqii.

3,-7 -3 16- 12-r-s 4 16 4.? 7 7

-(cos

sinr a + cosr a = (sind +

638.

u"r.,,@ =

"ino"*o

-2s5sin?d 2s3.

sEaMeEHrrR lra sin2 c[:

r" a. "t"t = ". "t""' ". """ "

o.ctg d < 0,

634. l)sin d + cos d=D; sinzc + 2 sin dcos cr+ cos2d=12:

nexax.

iCl'l g,t, 9I "tg1 =9,L l-ctg's 4 \ \4') 4 L t6r

O, roMy cos

sin2o+cos2<l

cr + ctg d = b; tgz u.+ 2 tg ct ctg o. + ctg! s= b2t tg2 &+ ctEz (r= 2)-tg3 cr-+ ctg, o = (tg d + ctg dxtg, (t - tg o ctg ct + dg;a, = = b. (tg, @ + ctg, ct _ 1\ = 6162 _ 2 _ 1) = 6o _ tr.

srn- ct

1) noAin{Mo qnc€nr,HnK

c > 0, ctg d <

635. 1)tg

2cos'n ?sin'o zcte"a-7 _ 2-(-2)' 7 _a-7 - 0,,u. "i"6c . 4 sin"itf., 12-8 l= 3 .os: a cos d 3cLg'zo'+4ctgo 3 (-2)'-4 ( 2f srn-

coE

"..o*cosc.coscr 1 sin (r

+ cos'tr)

aHaMeIrlIrrK sa coa ct:

2) IIoAin{Mo q cenl,nnx i 3HaMeEslIx l{a sin2

y IV qBepri:

iiliii:iijiiilii

f+J'

r"n,t'=. ;; "': (' 10000, -9?5 I '= 4/roooo ro _,v 625 s

AnrEEpA Mep3reKA. r. ra

iH.

AxaAeMi,{Hhr piEeHb

!it:

g95

640. Hexan trepffs ApyKap&a ApyRv€ jl: cropilloR 3a roAnHy' a 3a roAtrEy. IlepIIIa Apy&apRa HaApynyBarla 56 cropilrox

4 rr"p*u rr'Irpar{'a g "os"t.

solo AopiB'roc 2

Apyre

,," tI !9 - !9 ] roan* a r)

roAr!I{' a Apyra

""*"*,t'09 5 5 cropiBox 3<r roAets'

3a vMoBoro Bo{Ir Bxrpsfl'urti Ha 're

MeHUJe' ro 3a vMo-

a Apvra

- 4 croprEkr

oAHakoBufi cac'

z, ls, = +,,

0,6x x =I;

7. OopMynra AoAaaaHH9 sin {, sin B + cos d cos [i + sin

I-

2) sinSO'cosd+cos30'sinCr

1J3

i-"" 3) \E(sin

l./3 - "r9"'" " - jcoso Gcos45"

t; JZ v'"ina 22

(cos 60" cos c[

sin

sin 45'cos o)

l:r

sin 0 = 2 cos

cos l];

sin 60" sin o) =

sin 30" cos

"6sin

cos

t[ sin

osin

cos

30' sin

sin c. cos

d sin p) = coscrsin P= -2 cos

+ cos 60o cos

+ sin 60' sin

,,6sincr t coscr-.,6.slnc=cosc;

cosl17" +

((d +

sin 0 = cos (} cos p + sin d sin

= cos (o

30' = ;r

sin 15"

*""rU" =

uo' =

"r" P)) = co6 (q + B o u B]=

cos60'

"o"

2p'

: @: 5) = cts - so. 3 sin (19".41'l sin60' 6) cosocos B+ sincrsin ll- 2 sin dsin F=cos cr cos B siD osin p=cos(o+ 11 rsdr rep 2 a i,l Lr tl 3.2 6 645. rsrfl_or= = t-tga tgp r_1.1 8 8' 4 8 7

rsra Br

B).

cos 80:

P) (o - 4')

p).

24 tsp 3--l -o-rzs. Iraotao I35 = -316= -1= 8 tga -

o tel$.ff.)=te$=tel=r. 36) = te 60" = \6; tsd 30) tg 20. 649, lqo6 AoBecrr. roronisicrE,, 64A.

sin p;

Le @4" +

roroltrHi neperBopeHH.s riBoi qacrnlln ri orpuMacMo s[par. piaHr.rfi Bxpa3y. eKIrii croirb y trpaBiii qacrysi.

,, cosacosp sinasin0 rsinosinp- cosdcos0- ,. " r *- r "*,p "* r "t"0 "."""."0 " ".. "".0 - cos(}sinp + sindcosP -.osdsin 0 _ 2 sin ocos0 _ sin d cosp 2t rsocrsB. srnacos0-cososin0-sinCtcosB-cososinF 2.osos'n0 ; Jzcosc-z "jcosn+z 'fsinc 1E ros a - 2rcos 4 s.cos d - Ein 4s. stn d) Jt ". "' 2tsin45"coso r sinocos4S") ,[2r;.""- ^ Ji ^ J, sino Jzsind 2 -2aoscL- Z 2 - ,,8 "o" o -.,8 "o"" - Jz "tn- a Jz"in" = , Jz c Jz o ,72 "sui Jz .

5cu

43'l = cos60'=

{10' + 5") cos15' B sin C[sin 0 +.2 sin

cr eos

= 1' I 6, B) -' Le t27' 33')=--.1--=",nun"= te60' '-'-' 3'

' n ft l -l 3l J2tsinrcosd-cos^sindJ cosd -sind = E-1r v3coso-J2 -t'sinc coscr - sin..r -coso sinc cosc sinc=0i = lz 22 643. 1) sin(d + 4(I) = sin

p a + 0)= sin 2F;

2) tg

cos P + ccs

- (r- p)-

647, l) tE OA'+ 47", = tg60" = .,6; 2) ts (1" - 46") = ts (-45o) = -ts 45o

sin q + cosc[ =

(sin

(o + 0))= cos (s

l2O" 5") sin15'

cos

cos t64"

646.

€ tscosc-s:n,r r'osc sind coso-sincr-coso 4, 2(cos60".oso r sin60"sina) J3"ino "o"o = ,t; r...a : v""inc-J3sina-costr cosd sind'sinc-coso=0 =r 22 642. 1) sin o cos =sin c,cos B

sin

4') cos

BiAnoqiAb:7i 5,6.

1) cos c, sos

cos(c

sjn53 cosT -ros53'sin?'-sin (53', ?') cos53"sin7"- slnOO"=4;

6) sin ((cr + P) - (cr- P)) = sin(d + 7\ sin' (d + p) + cos' (cr + 0)- 1;

3) sin 75'cos 15"

5.6 15.6 o.8'r=o' y=_: x=t..u=5.rt, 0.8 [x z u:

2a 22.4 O.8 ^ 5,6-0,8rr ^ 0.8.r 0,8.r

641.

R =cos2 =0:

4) cos cr cos (cc+ B) +sin Crsin(d + F)= = cos (-p) = cos p;

2) sin (12" + 18") = sin

'2424, 2A 2A - -=t1

644. l) cos (6d 20) u = O.8.

l_^ -^ 199 4=z,z; x

1o aI l-=

/sz _+ n) \ a al

cos

9) cos

54 piBssHEa crcre*", ;= ,,

4-P= x

ro.au'a'. nppure prBstHHt

Ilepllla Apy(apxa llaApyr{vBarra

4ca ' roarn,

po6orv

Apyra !l cropilror{

"o"o

396 i::::: AInrEEPA Mep3ncK A, r. ra iH. AKaaeMi'{Hnf piBeHb

::ii:::::::i:

:':i+'l

"in

"o"o

:ilitili*.:::Jtit AITEEpA Mep3neKA, r. ra

iH.

AKaAeMi,{Hri pieexu

iiL:

392

I' pl {a-plr _ sinlo +rd-0)=!in2o_tn2o, cos{dt0 c-p) cos2o sin 45" cos cr + sin d cos 45" - (cos 45" cos o - sin45" sin 11) sinr{a -

cos((d-pl rld-pll

"iffi.1,

"E Jtms(I+ lE ;cosa+sina;o ",na sin s + 2(sin 60'cos d

;;;;ao'

,("*€o'

sinB =

1ri;:

cos' P, l

,12 ' .6c n rsind J2 J2 6)

*"P = ;,

J2SrnC

cos 60"

"- ")

sin(I-\3cosC!-"jnfl J3.*t 6".*,. "," "'

".-

\6"o""

*"o

t16

J2 cosa

f*"o -, "i"o*z S

sin d)

.f3

sin ll =

JE"ins

n 2.

--.." \t- 2b V2b

l"n,,

5' 5,

sino= ]f;

654.

3f a) F0r=cos,rcos0-",,.ir"'"n '

cos(n

]"1"o "6*"o

6-,--. \rrtPu'

"o"

o = t.,ii -

"i,,"

12 25

:a.];.:l

o; cos,x=-

"';

::::::i:l

o sinctcos0 = 6so. 1! " "oggllg:qqp lt! 8t9. = '' sin d.os U .os(1sinP ' srnPcosn "*""."S z.*.o"o*z 9"i"o J2coso -2{si-45'.oso .os45'srns) Ji...o 2(sin60'cos d rcos60"sinor J3.oso z.f"o"o * z !; "in o - .,.6 "o" o

.i!!r!

jn o

Jz"oss v2.oso' f sinc J2sino - ". sln d J3 cosd + sinq ../3 cos(x sinocosP ^ 2sin ocosB - {srne.osll - s;nlJ.osdr - 2sin dcosP .os{o + F) "' costo 0, sin0cos0 rsin0.os0 sin(d{ 0) -.g(d + 0r. = cos(d + P.) cos(cr + lJ) OSt.

"o"o

r.',[ "in'or "o"a=

sinrcr 4s")=srnc.os45"

,[H

ocKini,Rn

"rnpcosct

Kyr II qBepri.

./2 i 40\ , s"E rcosl:lsin45'9 -2 I A) "E242

40,t8

= .,/i:105f ,

ocKi"{blttt cr

9. 5

398

4%'

.osp Jr

sin

cosp =

t - e .lEe q: tslj^ 34 25 \25 5 - s5

^-.Jl cosl'!

&yr I qBepri.

3 4

5,1 3 3 '-

657. 1)

sin 15" = sin(45o

30o) = sin

45'cos30" cos45'sin30"=

_"8 y_"6 _,8 _,16-Jt ="8 2 "E 2 22 4 4 4 z) sinr05" sinr60. 4b"r cos60"sin45..

f 9 t ) " ^tt,

I I-=L te60'1s45" r-!6 I crp -ro5" €105" 1e(60'r45') rg60'+1945' Jf ' t /r

J:)(r Js)_r-?.@-B_4-2$ h,

i' ,lltt' "at- t-s

x]"r I .rBepri.

ii::: AIrEEPA Mep3rcK A. r. ra iH. AKaaeMi,{Hhr pieeBr

ocEi,lERu

kyr III

"i,'o=tJt-*""o; oclrirbrcn

-'1 3 tgo 190^ 5 2 tgla - g; I-tgd{gP I .lI.J^ 4 ,58 = 2. 24

3t ,

Iil"r IV qBepri;

liii:jlliilli::::i

ri:,:J

"11

t 1-Lg45"Lga I 12

"itt

297

-u/i: o3o = -"6,0n = -0,s. "i"o cos(60" - ct) = cos 60" cos o + sin 60'sind = l"o"o, V'"ino= ' t-O,Or !-o t-0,St 0.3-0.4J3. coscr =

105 192 17.% 17.%=

656. rs{45"+at=-lg1)'-Lgd -

-o,o; "irts = rn/il "o"'cr;

ocninb:in ll

t5) 7 ( 8l (-24 s,n,d-Br=q,nn.oqn-.^.^.r"n -----' ft 17) zb \ t7) \ zb)

es3.

"-p= !/r I ;l

sin 0 =

a2 cr

sino=tJr-cos"g,

6ss. sinP - :

B1\E

652. cos

-"0=1,

f , -J

-2

:lit:il:liltii:.rli AITEEPA Mep3neKA. r. ra

iH. AKaaeMiqHnn piBeHb

al:l

399

658. 1) cos?5" =

cos(45o + 30") = cos45ocos30

J, Js J, y-J6 2

rr is1-:sg lci-lcP tgd + tg0 iga - tgF

- sin45'sin30'=

4''E

h "li r 22

,'E

2 2

659, npoBoazMo roro*cEi DeperBopeHss niBoi aopiBllloe trpaBiii

qacrrl ii

orplrMaeMo Bspa3,

skni

cacrrlri.

sind sin0 sinocosp cosdsinp- sin{d-pl . 1) tgo igp=-osd -;= *o-"p' r ""ir"*psin0sinc costo 0) cosa sinB cosocosB---: 2r cls.r- rsL, " sins sLnosrnp sin(r.osl, -{ coslJ

sin

cos

cos s sin

crsind +

662. 1l cos2d

2)'

cos4.I

4.x

sin

cos 2cr

sin2c

sin( 20J

sin 2d

sin2&

sinz(l

2c - sin sin2c,

sin 2cr

sin(2d 4d), sin2q

4oo

666.

J3 cosd

)

- J2(sinocos45'+rosasin4s')=

sin cr =

+ 45") <

'6.

.,6.

(t" vrf

cos" -

, \ ;"* d] = 2i.os30'cosn

(30' + (x); -1 < cos(30'+ cr) < 1; -2 < 2cos(30" +

HanMer ne sEa'reslls

- sin30"

sin dr =

rE sin o +

'6cos

< 2.

rO[]"t.". f *""J =

1< sin(d + 60') s 1; -2nE s e sga.{egng

cr)

-2.

2\Asin(o + 60');

2,t0, si]lL((t + 60'\

<2\8.

- -2!6. :

667. ItorfteH.IneE apr.OMer*r.rHoi rporyecii, rorrrEaroqn MerII'rEr{M cyciAHix qnesiB.

apyroro, â&#x201A;Ź cepeAHiM apso-

t4x+5t-lx-+2t ,lx L Z, prBHsHHs: - - 24x 5 x" -2=l4x- 2;x'?-10x+9=0; rr"-10. .r. =9;.r"= 1. Ilx. r,+j2=91 1. r,=9;4 9+5=41; 7.g l=62tg' + 2=83, 2. \=1t4 1+5=9; 7.I 1-6;7'+2=8. ( Kia{eMo

Bidno?iob: 41, 62, 83; 9, 6, 3.

B);

ii:: AITEEPA MepsrrKA. r. ra ifl. aKaaeMi{Hrr pieexu

= 2cos

HanMen

^"' LEr(t ls29 (r'eo-tgoxtgo rtgp) rgo tgp tgo rtgp 1 r,e'aue'0 (l rgargBXI rl,gorgp) l rigctg0 r tectgp -

cosqsin60')

-1 < sin(o + 45') < 1; -'E < .,8 sin(o Haii6i,rrue sga.regrlg

663. 1)(sinCrcos P+ cos &sin Bxsin ocos B cos osin B)= = sin, ncos,0 cos, o sinr p=sin'c(1 - sin'z p)-sin'p(1 sin'zC[)= = sinl cr - sin'zcr sin' 0 - sin' P + sin' p sin'? d = sin: o - sin'zP; 2) sin' c[ - 2sin q sin P + sin'z 0 + cos'z cr + 2cos cr cos I + cos' - 2 = = (sin'cr+ cos'2d )+ 2(cos C[cos 0 silra sin p)+ (sin'll + cos'p) - 2= = 2 + 2cos(ct + p) - 2 = 2cos(0 + B);

= tc(o + P)tc(ct

= 2\E(cos 60" sin d + sin 60" cos o) =

(req+teB)=

= J2 sin(0 + 45"); 1

sinl.r 2dl sin( ([) cosrrsin.I cos ct sin cr

4cr cos

p) (req+rep)=l+l++ 1-tgCltgp I tgorgll r

tc q tc

lt; 6 2) sino. cosc Jz """ina-Y-"" 2 \2

cos 2ct cosC[ + sin 2 sin ct cos 4C[ sin

Hdn6inbrueJna,reHnfl

coscr

cin 2d qin o 1 cos(] =

is(cr + pxl

r -/t lr s:no Jacosa zlrsina 'i -s".J zrsi""*"60' = 2sin ({x 60"); 1 <sin(s-60")<1; 2<2sin(ci 60")<2.

sind cos

665.

rt cos0 coscsinp cosPsino sin{(r+lll 660' ctgq -"iep= = = sinc"inp " "1"r"""P "ino "i^0 c,(Id(td0 srn o cos o cos, cos d cos r o z=___t - r=cts t 661.1) z.-___J _4_; ct 0 I I ..r --"4 4 4 oos2ct sin2dcoso co62dsina - sin(2cr-a) cos cr .'r _ _' sinosin2d sinosin2d sinn sin2a sindsin2ci -sind cos0cos2a cosdcos2o 1 I ^. tt = = ;, {gf,n ro = -",}*+q re''n d "l"ry c"",rr' - d, "."4 ' cosccos2c cosci cos2d 2.r sin2d cosc, slntt

cost ct

064. 1)cos(o+F)cos(s p)=(cosC[cosB sin s sin Bxcos q cos p+sincrsinB)= ' cos' ct cos'? B - sin'2 ltr sin: p = cos' o(1 - sin'z B) sin'z P(1 cos? cr) = = cos'?cr - cos'o sin'z0 sin? p + sin'B cos'?o = cos':o sin'?p;

rg0 te! tgd 1gP

cos

]-.

sin75" = sin(45'+ 30") = sin45"cos30" - cos45'sin30" =

-2f,cL-' t-rsdrgF+r-Lgdrgp+2Ls,cL'

1-tC"teB 1-te"teP = 2 + 2ts2 ct = 2(1+ te' = Z. ]-= cosct

fillllltlli!!::j

i:iilitiitili_iati AITEEPA Mep3reKA. r. ra iI{. AKaAeMiqHlri piBeHb

iiil

4Ol i

{ 668. ItBaapar qreHa reoMerprqEoi nporpecii, roqlIsaloqlr

cvciAEix qresiB. CxnaAaeMo piBEsHns:

apyroro,

â&#x201A;Ź ao6vrlcoM aBox

(r- 1X* + 7r=(t 2x\'; x2 +7)t r 7 =l- 4t+ 4r'; i - 4tz+6x+ 4x-7 -l=Oi 3x,+ 10r-8=0; D=100 -4. (-3) . ( 8)-ai

I n) 4l srn14r! 15=srn\ fl--l=srn-. 15/ t5

= z:

-10+2 8 4 t- -1O-2 -2. 2l3'J ' 2{3) 6 3 25, a.!-t=!' r z4=-2.! -' " s'3 ' 3' - 3 3'3 z 3' ,, = 2:2 - 1=lt 1 2'1=-3: 2 + 7 =9. 1 5 25 - .li utdno6tdb: -. -t:-t:^^v. "lD

Moxce EatroBHgrn 6aceiE 3a J'

3a oagy roarHy nepna rpy6a EaroBHIoe

1 qacrrtrry TY

- 3a I ro.r. rpvoa 1 "t" z z* = ! *u. = 605

roA., a apyra

oacen aa, a.qpyna

rnny 6aceiua. ABi rpy6r HanoBslororb 6acenr ra ? roa. 12 xB. o"""ti"u. = .IlBi 1p)6 3a I loauHy HanoBHlo]orb

,'r

1.1 = 'rcreMlr: x!36 :.

i 4x i 6aceiiEa. PasoM rpaqmBana 4 roAlrstl i rlarloBErna ! 13 t ! = t. c*nanaeMo apy.e piB'slr,,n clrcreMrl: 5 |t-4t. |4

I' c

6ace;ara, a ,qpvra rpvoa

1) cos ct;

9) 671.

cr)

cos a;

1) sin

C[;

sin

Cr;

nll=-srn-.,r 4l' cos5n=cosl/n 0 \2-+ 181 1a

402

180"

n 30") cos30' 'r;

(I=o;

-ctg(x tgC[=-1;

cLg

ctg

cos

o + ctg

3 ts(180"

d= 45')

2cte si

cr c.tgq=0; -

2 .

sin(180"

- 30')

-sin q;

-sin 0;

2) te si

ct.

2)-cosC,+cosC[=0; 4) sin'c,+cos'?c[= 1. +

ts(360'

3ts45"-2sin30'-is60"' 2sin60' 3 r 2

cos (270" cr) = cos q;

.i,' n - J3. 3 2

5)cos'?lt+sin?ct=1;

678. 1)

ctg d;

,60")

2srn(180"+60")=

;-Js++=

60', tg{360' 45") ^. sin (360" - 45'.)cost360" zr stn{ro. + 30"r.osr1S0" - 301

sin

45"

cos600

tg45o

cos30'. (-cos3o',

l@l'1., 1.2s 4 s. - ;- ----=;' - \2)2 J3 | n3 2l z) r n' nr) , rr ' 5]J"'*['' 3) sinIn. "'(l-tclr rJ 4.]cosl'r-;l nr ir o nr r Gt ' 'ts cts l= Jo "D l

cte (270' 6) cos q.

672. 1) cos 123" = eos(90' + 33') = sin 33"; 2) sin 216'= sin(180" + 360) = -sin 36"; 3) cos(-218') = cos 218'= cos(180" + 38")

cos{

6) cos {:{ + cos & = 2cos

3) cos d

cos a.

3) -cos

.os I 50o =

cos

t;, 2) 4) 6) 8)

677-

(t-

OopMyn]a 3BeAeHHg 3) sin d; 5) cos(182" 7) lg dr

3)-sind sind= sin'd;

re_

BiAnosiAb: 18 !or..i 12 to4.

670.

sinl 5Jrl -"i.8= -.i"lzn ^l- I "i"nl 3) 3 3,r \ \ 3' \

676. 1)cos

11515113 | =-: u=12. 18a 36 y 36 18 I36

675. 1) tg21O'= ts(180'+ 3o') = ie30'=

BoHa HanoBHnrb Becr,6aceirH

U'o

a," )r u e 9 rg 1124, l-+-=l:

lir r 36 112 l-+ 4=I:

.os225" = cos{180" ,

3l cosi 150")

IlepIlra rpy6a nparloBara 8 + 4 = 12 roAlrrr

I II

2) cts 315" = cts(360o 45o) = -ctg 45o = -r,

c(rraaaeMo trepue piBrr'IrHs

45") cos45" '; t; 2) sin 240' = sinr180" r60') -sin60"--;: n J2 5r - cosfr ^rjr cos; ' snl -cos 4) 4' -Tl f a,r) 4n cosl/ rr+ nl n 4) cos \ 3.r 3 I 3l 3

674.

669. Hexan reprEa rpy6a

673. 1) tg 124" = ts(90" + 34') = cte 34"; 2) sin(-305') = -sin 305' = sin(270' + 35") = -(-cos 35') = cos 35'; n) '-l I 'l- tr\ 3) .rs{-0.?n) = - cue0,?r cr,el -1 2 r s) [ ''5, -"5'

cr)

te d;

cos 38";

iii: ATTEEPA MepenrrA. f. ra ir. AKaaeMi.rHr4i piBer" liilitlil:l:i::ii

6) -3

"3 2 \ 2J -'4 10" sinl20'r10') sin30" 9" sin(21' 9") sin30'

20".os tO" - cos 20'sln sin 2l".oE 9'- ros 21" sin

srn

i:i:iii{iijiliii: alresPA

Mep3neK A. r. ra iH. AKaaeMi.{Hlri piBeHb

iii:r

403

d ., "'

cos66"cos6"+sin6'sin66" cos(66' =

"""65'-."5"-l,tr5'"1r65"

6")

""qAt'-S"l

cos60"

679. 1) 4cos(180'+ 45") - 6cos(90'+ 30") + 3cte(360" 60") + tec80.

=-4cos45"r6cos30" 3cr.s60.+ tg60..

= z"E+z-"ls+"8=a-z"E; 2'

6cos'?(180'+ 60")ctg(l80" + 3o')

"i"fzn \

- r'J-"1' 4)

6111 6cos'60"ctg30" 12)

.,6

l,'l n,nl".nl \ 3./ \ 3/ -\tr'6.] =-srn4 l-'os3.]te3 n e ali

Jzlt\

2 \ 2)

4')

60.) =

-4 f t 4-.n= 'u I

cos30"

-sir(270'+ 30") (-1)'

683. 1) ts 10" ts 20" ts 30" . ... . cts 30' cts 20" cts 10" = 1; 2) ctg 15'+ ctg 30" + ... + ctg 90" + ctg 30" ctg 15" = 0.

...

cte6

cos64'cos4' sin4"sin640 cos(64o-4') cos68' _ cos68" cos71"cos41' sin41'sin71" cos(41'+ 71") cos112" -cos68"

680. t, -"ino "o"o--= "]no "oto --"o"o' -tgd (-cosd) sln0 cosq

coso

2\ sin F sin p

cos

B. (-cos

P) =

082, 1) ctg 55'; ctg 65" ctg 75'; ctg 85" saMiEnMo raEreHcoM sa ibopMynorc .rg (r tg(90' a). oAeprRrMo: ctg 5' . ctg 15" . ctg 25' ctg 35' cte 45' ' tg 35' tg 25' tg 15' . tg 5". C$opncralmrcE OopMynoro tg cr ctg s = 1, orpr.rMa€Mo ctg 45'= 1. 2) TaHrencr ryrrx KyriB saMiHro€Mo Ea raHreEc rocrpnx EyriB sa OopMynob tg (180" q) = tg (t. te 20" + tg 40'+ tg 60" + ... tg 60' tg 40' tg 20" + tg 180'= 0. 3) CBopnc?a€Mocr lbopMyrrolo sin(360' d) = sin o. sin 359'= -sin 1"1 sir 0' + sir 1' + sin 2' + ... sin 2' Bin 1' + Ein 360" = O.

sin, B + cos, p = 1;

oea.rrlLeln'Il ,\'.4)")\"|41.)"rs"l ,loel z' 'l "ig"l * -.is"J = {1 + ctgct'? - - cr,gcrJ'? = | "is I "ts"J l"rsI 11

= 1+ 2ctgd +

( sina coscrl . 3) coscrsrndrrgc ' crg0)= cosd srn dl* "o ",rol sin?a+cosra = coscsin d

1- 2ctgcr

-f

ctg'cr =

t r/ = 13 ' -t2 -1"-"t] (" )l '-"i,.1r..,1."1,,[r '6 "\2" r6 d 1) ,(

.tq'l

l:t-

I I "ln +nll ctg- /n +{11= : l srn-L -\3

.ln

13 I

)

.i",f" L3 ' ") ".",f' ' """,1r 1 l sin'"(n + cr) \3 l =.i",1 I *"1 **",1 1* = r,

\.3 /

,l ft i '"' +(I"

cosc,sinc,

at -sint"-atslnl " al. sin'rn-atsin2ln+at cos'?rn 2 '"r."*'llI-"I= \2 ) \2 ) = -cosocosd sin2 nsin'n - cosz crsin'cr = -cos'd sint s sin'ocos'c = o(sin' n + cos' c() = - cos' o - sin'z c{ = - (cos' .[ + sin': q) = 1; -=1; = - cos' c( - sin'g 5\ sit" t + tg' r. clg', + cos r cos, = sin2 r + cos' r + tg,.r. ctg, n = 1 + 1 = 2; 6) (cos t + sin.r)'+ ( sin., + cos r)2 = cos': r + 2 cos r sinr+ sin', + cosz.x - 2 cos r sin r + sin'9 r = 1 + 1 = 2: tga ( cosx) ,. ".' cosr {-igr) -' cos' .r ^ .:_+-t_ sin'r sin_r sin..jr rcos"-r I. dt + sin'.r " ctg'x tg'.r I sin'r I cos'"r - stn sina qigla . 681. t) coss; teo ( sin0)= -!!!a1 cosd 2) sin r.sin jr + cos r. (-cos r) = sin2 r cos2 r = -(sin, r + cos, r) = -1; ^. -tgd (-cGd)ctes = tgd cosd crgd "' (- rgox cteol lgc cugc 'l "."a "o"o 4r sinq crso-coso-"'"* -"'it I cosq+ sino= "11", ' cos9 I sinq I sinq = si g' cts cr (-sinel cosd ctgd ( cosq) sin d ctsd (t) - -Lga=Lgo- l ted l. - cos - ct ctg ct 4o4 l{t AITEEPA Mep3rrKA. r. ra iH. A(a,qeMieHrr piEeHr iillt::i:itiii:l

crg's

sin. sint

- sin' o(l t

-sin'zcr(l-

sin'?Cr)

2sin'ocos'd

;r;:

slnt

)

cos':

G;;.d) sint

sin'?

"t".t-1-."", o

- sin'crcos's - sin'

sin'? o cos'

cos' cr

crxl

+;tcr)

sin2 o cos'

I cos'za _ I ctg.11. " . 2 sin'0 2

.ln'- lrn\ 685- eos"' .""'-' " - " l* lt ' "".'l \2 a) """' !2 11,/ 8' cos'",

)

t3 "l)

crl;;5,g I

"'\

8 r cos' 11 - sin'? 11

-t

::iltlliillltji:ia AITEEPA Mep3neK A. r. ra

= 2.

iH.

AKaaeMi,{Hri piBeHb t::::: 4o5

t. l.

t.y

cos'1" \4

sin:170" Fd'

sin {70'+

tra 5 ro,q. 2

flrir

+cLs{so.-rr}cls(8o"-crr=r-crs'r8o'-.rr=

;JGo%

cr)

BnpaBx

arc

r'+r--6-0:x v-2

690. 1r

rx tii 0ir.r=-J: rr=2.

SaMiHroeMo HepiBHicrb piBllocrrrbHoro crcreMoro:

)\x 3\x -

2)tx

lir 2,0r (.r 3X-r 2)' BianBiAb:

- 2t. 0. Irr-3xx -2r' -

x, 3i.r2 2.

3; 2) w (2t +-).

BaMiFlo€Mo HepiBHicrr, piBEocun6Hoo clcreMoro:

lr,*

ou*.

1,,

!u'

Bianosidb:

+)/-T-V -V34 t 1

rxr ;xr-r,.0. 2r,r-ar(r-;Jr'-rr'so. l "

(!: 4

L..

I{M/roA.,

roA., a

= 3.

21 2qin

- cos'; "a - srn'-i "q 3)

! sin'z4cq

11"""1,-1), 2.t"1, \ 12) \ 12)

"".,1,{ \.4-,

sin2

d = cosr

ts'1,5q '

sin2ct z) '-"= tgza;

?!i19!9!9 = 2"o"o, sin,

I -",",|.1-rn.), t4 )

2tg6s 1-i8 6d'

ts3.50 1- te' 3,5q

o.l

2t91,5d.

6e2. 1y

.r-B.m n-B : 22

41 ?!1l25""o"25'

2aos25"

"tn

rr",

, cos" 22'- sin" 22'a sin'z22" cos' 22' - '' "' "n.'zz7-;*22 rsino) sintc tcos(}-sinaxcoss - cos'c t,t coso - srnd cos0 srno 7)

i,",'

6ss.rr vr-J2 |t-2.12-l.,l2l =Vr-J2 i/(r-J2) =t/r ' Jz.{lr Jzl = {r -Tz r(.n - t)(o r) = tD l = Vi = r' zt :,lr . z.z.1s. (v:r' dtz v:)' ..,/z V: u{z - Jr . - Jr -

.,,/zl

lz - 'axz - "a) =.ln-s=ur=r. 406 r:i::: AnrEEPA MepsneK A. f. ra iH. AKaAeMi.{Hni

691 . 1) 2sin 5cr cos 50;

9 sin'9: 22

--:{, 1-tA':'

B) cos,

-l

lTj

^. trl-.

ra ;

sin 1,5{:! cos1,5q;

2ts

3) r:- 3r- 4 = O, tt= 4i x2= -1. 2x' - x - 3 = O: D = 1 + 4' 2' B = 25'

1+5 3

cos'?

4) cos'4o

i 2/ol

g. OopMynra noABiiHoro apryMeHry

lrx-5rrr+2r>o. x(x- 5Xx- 2)=0: r,=0: x,= 5t xx= r.r0; BilnosiAb: | 2; 0) u t5; +-).

6..0

BrAllicrr,.roBHa (n + 12) nM/ro,q.

+ 12) l3.r(r+12)*0; se sa,qoBo,rLHs€ yMoBy sa.qaqi; 45 = O, t, = -I5 Orrrie, nBrrAKicrb nnora 3 nM/roA. BiAnoeiAb: 3 t<M/roa.

SaMiEro€Mo EepiBdicfi, piBHocr.nr,Horo cncreMoro:

t-2

20 xM

r' + 12r. -

-:2l* ' r-2

3!(x

noBTopeHHs

lo zs; t' -rr 3r Io -o 'o-8.0, txt .r'- 3:c - 10 = 0; \= 5, 12= -2.

6g7,1)

noAonas 20 xM

- r

xs.

oi"'**.a

roAi ,n soscH oa '"r2 'o4rH. n,Iir 6yB y nopo3i 16 t20 20 \ roa. b'nhlxe. Do 3a yMoBoro -1 aoprBH$c b roa, ", L _ I t2J -,o4. t6 5 5 4 (-xnaAa.Mo piBEflEHfl: 20 - 20 ; ,- n- :t .4i , , , .12 3i 4'' 4sx + 18o = 0l: (-4), 15r. + la} l't - 4r' - 48j. = 0, I I]nir

---L sin (80"

".r.

sa 12 nMhoa. 6in6ua

Hexafi rnBsArcicrE nnora

= s|

tIoB€H

,rctg

srn'f/u- + 0)

689.

l.\

rolt rsin' 'l l'l r( sjnsr.coss.iso \2 \4 "lt) .(n ) . "ln ) sinscoscr sinq =cos'lz+dj+sin'la-".1I """"=r-srn'd=cos'c: sin':lgo-- t20" - d)) 2) clg (90" (q , tu {8u cr)

6a6.

"/z

piBeHb iil:i:li:i!!ii!:i:ll:

2 sin c, cos cr

;?s. "jts = I cos0

'r 2-*i**

sindcosd ,2. -=cosa-stnc(;

2sinccosct 2'

i:iliiiiillllll: UTeSPA Mep3reKA.

r. ra

iH.

AKaaeMiqHri pieexu

il:i

IOZ

10)

sin'?

I -

zsin e cos

cos'? Q

+ 2sin

cos q = sin'? Q

r .o ,") rr) sjn" a .os'7= l.os" 4 -srn'41 ^ |2t' 2sindcosc sin2s 1.t-p- za.i 2 cos2o. 2cos2a 2

n r:lr I '"' I-.os' I ft - c-)I - -"'\4 "in'

= 1;

ar I

as" = "i" 24

cost:

5) ts330'=

olll*"'1" t '4 oll = ,rl r4 or-"i"'1"

["--14

+ cos'

([

sint n + 2sindcoscr + cosz

2sincrcosct

2l.c(4-5'

2(l-LE

d) !!er90" dj = 2

@5" + 4sin o cos d(cos'

16) 693. 1r

sin:

cr +

-; . _].rezo;

sin'rr+cos's+2sin'n

lst'

. 2cr

cos'c( ,li

o) = 2sin 20 cos 2d = sin 4ct.

sin'z

OgZ.

cos'g35'- sin'35" _ (cos35'- sin35')(cos35" + sin35') cosB5, sin35": = cos35" +

sin35' 2

cos35" + sin35'

si19

sin'

cr + 2 sin cr cos cr + cos2 cr

11)

12,

2sin 2.!

2cin2dcos2d

(sin'o

cos'?

1","f1 (cos'(p

13)

crXsint

,".]

asin

cos

I.Sa I

cos'?rl)

sin'(B 2

cos'

= zsin 1,5<rcos r,5a = sin

a5"))

sin

t.lc ,

-tg(180'

€' = tero'='T, r nt - n Jz

30')

cr =

tr,6 -

"innyr II qBepri. "o"'cr; "in

2.r

e0")

"o"1=

sin c cos cr

J0,64

0.8.

0,96.

cr =

5\- 212.( r3 \ r3l

t2o 169

cos

cos?

sin'z

I ri -"i",4: c"s'c,=r l-r' \ ;/ =1 16=16' coszd cos- 0 .srn", c 15 r l'1 15 I 14 16 \ 4.r 16 16 16 2lgcr 2 4- I 7oo, Ls2ct " - l-Lg'd - l-4' - -15 -815 .

699.cos,cr= r

cos(28

cos

cos(e0'-

2B) =

-sin

2B;

sin 2d;

2sin 1.5c. cos'1.5{r I sin'1.5s .os

1.5cr

cos'

l,sa

3ct. aO"

zot. tgn

-l;

tgc'=

I ll \2)

J3,

i::l: AJITEEPA Mep3reKA. r. ra iH. A(aaeMi'{Hnr piBexr liiljiii}.i:.:::ili:,i

l4 , I

702. Cnoprrcra€Mocfl abopMyraMn 1+ cos2o =

co" 30. =

3,'62

4o8

d.(-

694. 1) sin 150" = sin(180' so') = sin

t,t

=;:

! I Gcoscr) = 2sin l,scr.f, sin l,5a .-. tbl-:tl+-='

cos

=-=r<in2d. coR 2.r .1

r"."ro.

- a5"))

14)

zJz.

o I cos qi sin'o , U' i1l' 8 1 8 ? .coszcr = I l3l I I I I

=:l4 sln 4ct;

cos20

z"tezo"

698. sin?

2q ,. 1-.i. r" ' 1+ sin

1+ sin 2ct

1 10) :sin2 2

te150"

sin 2a =

8) ' "6=9 '= '=ta-; 2"".'922 z"os9 z e)

s.y 1te30'

2te15"

-+;

n' -12"..'a-rl- -"..r - -G. \t2)62 .osc l-163y oso. "o.o o-,/l &yr "in'o: IV.rB€pri. oc!ri.r6&a sin 2cr= 2 sinocos s = 2.(-0,6).0,8 =

2sin40"cos 40" _ 2s.n40".

2";n9

- 30') = -tcao" =

6fl 3n ^. ;ll " srn " 8 " 4 " \"

cos40" 2) cos 11C[; 3) cos'2P - sin'2P + sin'20 = cos' 29; 4) sin 40"i 5) cos 204; 6) cos'z3c[ - sin': 3a + 2 sin'3cr = cos'z3Cr + sint 3q = 1; 7\

te(360"

695. 1) cos45"

cosl; - 2dJ t=sin2nr

14)

- tg,

2{r

€,

1\ 2 4)

si.n' 2ai

cos'z

d + 2 sin

c{ co6

2cos"

f,;

2c'ltl

sin'z

cosza =

2su."I

3) 2 sin'z 25';

d = (cos d + sin o),.

lt:lt{tiiiliilr: MTEEPA Mep3re(

A. r, ra iH. A(a,qeMirHrt piBexb

tit

4o9

703.

z.:"'!9, 12

3) 2 cos' 2o'l

2\ 2 cos' 60.

/.'a rcos fl, cos'zdr'sincrcoso ""sa). sinzd =2i \ coso srn ct / cosd srnc 1+ tg 1 + tgs 2tlo ,-r-. -"--' {1 tsq,(1+tsa) 1 ts:d

4l cos" Zslno coscrr sln' d = r cos-c/- srn0l 2J 4 2 2 4 ! 2 1 coslox 705, zo4. 1) Lg19s;

2) 3)

2' cos(4iu

- 30').

1+ cos(8x + 20')

sin20sino l'sin2a sincl

cos':C[

sin2 o =

sin'o +

sin? cr

1 cos(21o" 2.x) sin 2cI = 1 + sin 2C[ - sin 2cr = 1; -1 + cos' 4cl sin'2 4o cost 4cr + cost 4cr zcos" 4d 2sin40cos4(x 2 sin 4c, cos 4c[ 2sin4(tcos4c[

,""(;

3,'

"Ez,E

cos'cr + cos'

n 2sin'

r'.

ii::::iif.:il

2 sin' 9

:i.l;:iiis i!:d.::i.fl

;r)-"tl'!l

2.l + sin 6.l sin sin2dcos2c[

cos 6.I eos

= 2ctg 4di

2C!

- =2(os',r 2

r.i"'92

711- 1)

sin a cos

sin'geos: q

cos20eosd

2 sin' 9

2sin'9

7O7. 1\

sin 2d cos a

cos2dcosCt

= srn zc[ cos2dcosd sin(2c - (}) {sin'z a - cos'9 crXsin'? n + cos' a)

cos2 cr = 1;

2aos'2a

cos

sin2(lsina

cos20coso Icos2o cosoJ .os2acoso

sin2dsind

2-in'?3a --- 2 sin 3o.os 3c _ sin 6di 2l cos3d sin30 1 .. I {cos i:, sinr o) I cos'c + sin':c sin^ d + sin'o zsin':o _ ". ' "' sin cr sin'q -"itl" "it " 2 sin' 20 4\ = ts'2c1.

7O8,

{I sin' q) = 2 sin 2q cos 2q = sin 4d;

4 sin o . cos c[(cos2

7) 1) 2sin'zo

- sina cos2d sin':d cOS' C' COS O

l"*61

t+"o"1 3.

706.

lg':fl)

4Lgotl / I

2cos20 c( srn d sinq cosd .os

2cr

,",.11 ;r-.f

1,;t "''l; "l -."

cos(6cr 2([)

2cos4cl

sin2c[

cos

2 sin 2cr cos

2coE2d 2cos2d sinacosd a sin' 0 cos 2d -t

cos"

sin

2C[

2.os4d. sin 4c[

s)n Zoi I

scoss

Lâ&#x201A;Ź?c-,tga- lg'ct Lg2o: ,21g.! (l+tgdxl-tga) l-â&#x201A;Źa -= cos cr sincrcosfl rcose rsinocoso 2sinocoso 2coso 2sindcoso (1 sin0)(1 sin 0) I I sinT o t9a__-

4sin d cos'?d

709.

sin d =

cl'

5) 4

3' 71fJ.1'

sin30cos(r

cos3d sin (I

*4?,(;) sin(3a-cr) _ srn

_=_ 2

utJ,u,d 2222

,,d

41o lil: AI|EEPA

srn' 2

sin 2cr

24 7

2sin d

c[ s1n g cos cr 2"i. d ... d

cosc ..

cos

-l ^dl l cos' sin" 2 2)

=_=4srn(I; cos2c\ 5l /cosa I I srnzcr = cosasin2d - sinacos20 sin2c[ sindsin2d \sind Ein2d, _ sint2o o).fin2& _ sin0sin20 _ I. sir(rsin2(r sin(lsin2cr 1 sin (I cos'o coso 1 6)' cos'? c - sin^ c + I - cos' n =--=--ctgcr. -siD2cl -2sinocoso zsinqcoso 2sino 2

2eosd

cos'(

1=.""1\2 Mep3rex A. r. ra iH. AKaaeMi,{Hnr piee+ru

:i{lil{:iiii{!l*

n, ln \4

zoll lr+zaI ,.1 -"'ln-ln*zoll ') "o""Ir-zc'I-"o" \a \ t4 ' '4 r - zo t , r zo l = -lt*r"rJ', ="". l14 , ",,,]..^ t4 zol """,1n ' "r. t4 \2 ,4

zr2.

tsdi

;J::t{ilttii{i

arr I = )

"in

acr,

AITEEPA Mep3rrK A. r. ra iH. AKaaeMiqHrt piBeHb ::::i: 41

TI 2cos 2C[ + cos'z2o.- Ein'2.,=(1- siil'z2d) + 2cos 2s + coEz 2a= 2q + cos2 2a + 2cos 2c, = 2cos2 2c[ + 2cos 2ct = 2cos 2s.\1 + cos 20) = = zcos 2a . 2cos' d = 4cos2 d cos 2cr; 2srn2 2d zcos'2d 2sin' 2q 2cos' 2(t

2) 1+ =

714.

!r1q * ig:lli

sin'?

15'+ cos' 15'

=_=_=_=4 2 cos 15" sh

15' sin30" 0,5 -.- sin?5" ros?5' sin'/?5' cos/ 75" -2cost50. -cos150, cos?5' sin75' cos75'sin75" 2cos75"sin75' sin150" = 2ts15o' = -2. ts(180' 30) = 2ts30" = 2J3.

cos'z

I tg'2ct ctg'1 2ct I I cos'2d sin' 20 2sin'92c[ cos'2q 2cos2 2d sin2 2d 2('os'20 sin? 2cr) 2i = 1 cos" 2d 1 sin'2c 1 r sin2c-{cos'o sin ct) 2sin':a+2sins.osct 2sjno(sino-cosd) t'l*"in2ct*("*'o"in'o1=z"oJo-xino"*o2-"o"ot"ino*.o.ol

716, cosd -

sin

:, :t

ni,aHeceMo o6rABi

qa.rrHH 40 nBa4para:

l, sin'za-2sindcosc ' "."' " = I

1: q -sinzo 999sin2c=1-tr sin2o l, 717. cosg-sino l-"ina 2 2 2 "o"'9-2"o"9"ind 2 2 2 ' "in'a2 "1, 4 I

sin? 2cr - 4 cos'z ct 4sin2 o cos'? c - 4 cos? cr ' z"in"z., g"into s"in'o-" o g"in',* cos'c 1 , 4cos'!d(sin'0 1) _ 4cos'o'( coslcr) 2s1n'n 2 Ssin'o(cos'z (} - 1) 8sin'ct (-sin'za) sin'? Cl

- 4(1

I Ssin'.[

co.I '" lr : -

"' 2*"'

sin'?ct)

cos'2cr + sin'za

4d __ Icos2cr

J'_-

sin4ocos2d 2sin2dcos2dcos2d acos'qco"'24 - 4cos'crcos'2c

"-%""'2,a

4srnqcoscr 4cos'?c

cos' 4c cos' 4c cos'4q " tg2a - crg2rr sin20 cos2a sinr 20 cos'?2q cos 2s sin2c cos2qsin 2c I -" cos'4s 2cos2asjn2ct cos'4d sin40 '"'--:::r 2cos4ssin4d '- -:sinEo. --:-. 1 -2cos4ct 4 2(cos'z 2d - sin'2d) 1 -4

zr3. '- rr,-sin,lz+1"

l',4

r, - "in' I\ " * {

- a")|

I "i"'[I '4

tr +4al= cos,ll ln noll -') - -'-'q -"j,,11 t \4 *aol ' "in,l 12 {a l

= coslU + acJ

2) 1 =

2 cos

t4 "i,''f\*lol

3cr

3(r =

- sin'

2 cos

8ct = cos'?

3s(cos

3C[

3s + cost 1)

2sin,4 = . +sin, Sgcosiro; 22 2cos'2d 2cos'?2c cos^ ct sin? c

acr

2 cos

''n'2c \ ' ^"-o"'ro' 1+ tg' 2d. 1* "i": ?" cos'2C[ - sin" 2a cos'z2o, sin'?2o 2sin4.r cos 40 .n.2 2a -. = zsrrr4d. ^ 1 cos'2c cos'2c cos'20

:{l - cos0 sind -"." " "it2cos2dsin2a I

2 cosz

sin cos2c

cos

4t2

sin c, + 2 sin

cos

a.r

4 sinn C[

4cos2c-4sin'ccos'a 4cos'a(l-4sin,d)-

cosf 'r

\4 - / (n \

""la

2ct "t",

cos

\4' f

"lI

coE20.

"'.l." l4

"""1' \4 - "l)

")) "i"11-2'l t2 )

cos20 l

cos

719. 1)

2sin acos

= sin

o nnc': o

2 sin

-^ 4(1-sin'3d)-sin':q 4sini cr sini q.

sindcos 0

sin'2a+4sin{I][-sin'2d

zl cnq'z

cos 3c[) =

sin, 2a =

-2cosBq

2Ct .

2sin r 2sinocosa _

41 zsin4d ll-Le'2o)='"'no"

2 cos 3cr =

3cl(1

r 1' 44"t.'o=9.

2"in{l*"o"q] zcosa+l-1 2(coso rl) = "ino, 2) cosl q 2sin'scos'?(t+ sinn d 4sin, crcos,o= (cost o sin, cr)! = cos? 2cr - sine 2cr = cos 4cr; cos 2c cos 2d cos cr 2 sin'z .r cos {x cos 2d. sin 0 ^. -----ot = t : cosq(1 2sin'zcr) sind 1

218. tr

sinsa:

3s + cos'z

2 cos

2 cosz 3c[

. \4 a"l = t - "i"'fI

+"1

"i,'o

c[ coa a[

-- cos d, 2sin'9, ,2u zsrnq(l ,"tr ot1- t) = ,"-+ q ='ts t "."

it:: AITEEPA Mep3rrcKA. r. ra ifl. AKaaeMi'{H!,ri piBenb :i{L:{tii:i:;ii

".".2d _

f".":d \ sin- c

cos 2ct . 4 sin'2 c[ cos'9

"i'1qq/I

cos"

sin2

s . (cos' s

cosa

sm_

- sin' a)(cos' sin':scos2q

l:ifii:llitlil:il AnrEEPA Mep3rsK A. r. ra

ct +

iH.

sin'?o

t[cos".r sin'

a) cos2ir 1 _ 1, 1 Acos2d - 4'

AxaaeMi{Hri piBeBb i3l: 413

1 2ficos 4n lisrn,Tcos,rcos

sin'3ccos" cr cos'? 3c sin': a srn'.lcos- d

c[ -" sq!]lg)c'" tryg! "l *g:qS!qg) = 4sint3s .arsinl3./ rat ,1q1@ !l1o 4sin2d 2sLn2scos2a=8cos2d; sin 2ct sin'?2a sin? 2(} (sin 3d cos

cos

sin -2-222

a[*",] "'" ;)(*ui''"*']] sin

+sin

sin'o 4.4sin

4"t" ;1"'"';-r) +.r" i r"-'la! a"r''!"""'! a[r .r"'!J a-"']1"r"'!-r)

?20.1\

I _

4.W

sin

= 2')

2sin 3d

srn

sin72' cos18" 1 - 4'18' 4cosf8" 4'

2n I

4i I

- sln 4n cos 4fi _9_ I =_ .71

srn

\ -l9.r sinl 99

8,7

e n

2sin3d

12(I 2

sin6qcos6clcosl2c[

2 2sir''s.

2.4 sin

3cx

2sin54"cos?2"cos54' sin108"cos72' 2aos 54"

sin(180'- 72')

cos

72" _

2cos54'

cos'o)'"=

s) I

sina

utrespa

8"o"'o -2"in^c tcoso) {l "o"ro' 4(1 - cos ct) - (1 2") S"ir,,!_Z"tn,o "o" 4(1

2\ .r'sl 2l "-.'sfr = s.i"'s[ -.'sl

c + 2sin:

2sin'9 a cost

cr cosz cr

al + ({/a b) z:la b

qE-.tE.b

+ cost a

_ = ...2 qin'...d.os'

. "d'

,d'=rt,s''2

- 1- 2sin'ncos'cr a =

1" --cts'ct. 2 "

'{a + b

\:la+b-!a-b)

IE-.\E+b

! lrlf'+bb '

16-

(Va+a-Va-a) 3Ja b 1!o+b _ _,: a = lCn lo t to+u \tla+b-.9!a+b)

{'4.

0x 2 <o; 4\ r+2<O. 31

3srai6Ha kirLkicrr, DoAiii. IlinbKicrb EoAifi, sld Ba.AoBonbnsrorb t'MoBy A. -

1) -4 = {noMep KBaprnps, repEe qrc,'lo};

N(1) = 20.

I!l:!

prat = ?9 !, N402",o, = =

l(Bapfiipr .rrcro, 8 l, NrBr = 8, Pr-Br 405 3) C = iEoMep (Baprr,rpr

cos72' sin144' sin(180" - 36' 4cos54" 4cos54" 4cos(90'- 36'

;::*

2) B = lEoMep

2sill 72"

N=40. 2.sin12cl'cos 12ct

8 sin 3cr

(Va +

ite:

N(.4)

sin 24(x

721- 1\

725.1\2x-a<O: 2\2r+6>O;

726,

I .. sin ll

cos 3c[ cos 6ct cos

llsrn'"d .os""cL

,d - ,c .d asmasrn- cos' 222

724- 1'

2sin36"cos36"

.( nl srnl JI

sin

2cos18'

>lsrnqcosn2a4T cos I I -.

1 ^ cos2d '"'-- =::cte2o.. = 2si.n2d 2 " sin18'cos36'2cos18'

Zsin41t 4n 7 7_ ,11

(sin'z u + cos:

")"""[! G.")]='"'[i-,"""(:-") = "'[;-*) '"'"Il 2sin(30 2Eir2a 2sir2.l d)

223, (sin'(r ,"o"'o,

.,;i (-s*il =.,"'i,",e, ' *"

*",; [-*",]J

13..s'

4ft

-sin 7__1

--^ 3. I t4cosrr+.oszd-l 3+1 4cosd+cos2&-1

1,$n u;

22 1

(n) |ttn+.n

')d

.cl "c 2 2 ,u. ao cos sln

cosd t

4sin

7777 .n

Mep3neK A. r. ra iH. AKa,qeMi,{Hnr

NtCt = +: PrCr =

pite"o

liilllllliill

IiparHe 5);

Maâ&#x201A;Ź oaHaKoBi qv

Oprli

a. -{ 40= lo

i:iifliiiii:ilif uresPA

Mep3rcK A. r. ra iH. AKaaeMi.rHxt piBeHb

i:;i:

415

2) cos 15" > 0,

. 3r rs?b"= "

15" nyr I qBepri.

sinlso. sinio. r.1, r z t..os3n. 2 | "61 2t 2 2 J3

I r.ost5o"

1.(r.,6) (2_J3l(2_J3)

=lj="*,0' 4) cos 75" > 0, 75"

728.27O' <

zcr

< 360',

2ct

- lcvr IV'IBepri, t..; ti

cos 2 q

-J,-; Iz Y| "o"zo,.,t-"'"'zo-J,-l sin 0 > 0,

729.

18O'

C[ xyr II

< cl<

27O',

rcvr

III'rBepri,

'... ; - vol 11 l a 6\' o L coso -!r Itr -!,a= {r-

cos

"o"9.0. 2

d < 0'

732. o' <

Ryr II cBepri. I

< 90'; o'<

." - lJ -

@" Z) ,,

|;,",'lr=ryj cosl

Lc'{T-ol=,u'1"-ll "11,, -

I cos225' I r cos(!80" . 45") 1- cos45' , Jz tz lz\ , _ _Jz(z _lz\ -rQ"."\

731. l)sin

416 lil

r,' 8 ,tzn-ol I-l-, 3J =n,rg'1 o ' ls"

15"

",.[n'" - il '

*vrI.rBepri,

"'(,r-|)'o'

- """(ro',

vl-slng

AKaaeMiql"r pi"err lliiillililllf::J

-r."(ro" -

.{,

.r,

"o"ln-9J \4 2)

{l+sinq

Ji-si"s 2sin.r

r.u[+

r.,/i "l" "l" - "ir* f + "ir " o

v/i

r/2 cosa

="1-"(;-91-r"*(;-91, n.,.o, .,0, r<9<1.

816 t z ,;=s's ,-, \3// [ :

iH.

'/t+"i"" --rffi-_--rffi=

+ za)

4 2 2

.6. ","[l-tl \4 2)

q Jz r- e]l= 21"i"r"."I 1 ql , 4 t4' 2t)tl" 2t 2 "i"{ 4 2') t 4 \4 2t -"^"*l \2 = 2","[l - l - e] = 2"1"(l - e'l = 2"".e. 2 \4 4 2J \4 2)

l-e1,[ J2.".1\4

I{vr I qBepri.

MTEEPAMep3ntKA. r. ra

Vzl

;<45';

Ryr I qBepri.

l+sincr-l+sin.r Jz Jr sin'c

cos'2c=

' .,I sin; ,f2\ z J, l, J, Jzb .Lz) 2J2 2 .-8 ^ r*"."n4 2 \ 2t 2 2_J2 12+J2)\2_Jz) 2 2tJ2 tt G , - 2 -,'-''

730.

sin{r80o-4sot -sin45. .E f,

_jA??q

=-;E-A=-6-1il6;til="Ez 4

qBepri.

, l.

Ls112.so.=

* xyr I .rBepri.

ili$illltil

yci rAB

AITEEPA MepsrrK A. r. ra iH. A(aaeMiqHrir piBeHb

l0M,!.

{ll:

417

lr 1O. CyMa i pi3Hxr.lt cr,rHyciB (KocnHyciB)

3) sind -

1) 2cos 35" cos 15'; -2sin scr sin( cr) = 2sin 3c, sin (r;

733. 2)

_t t

, z"r"--|--.--f "-1-o ono,o = ",'l] "J -

z"intr"."l c.-rl=2.@."..1

2"i,5P"""f-qll 2 \ 21 2"i"5q-"8, 2 2

4\4)2\4,r\4,/

i"; 5n Zcos5ncos ,'I '2cos "72'"cosl \ 721= - '72" 72' - tx r(I) (r.-d) cos{r ts) tr -(r) ^zsrn.rcosn: 2sin --, {a 0t-(a+0, cos {o ll)-rd+0r ._2srnscos( F)= 2sinocos0: -zstn 22 nl tz. -\l-lz. r:o-"J 3' 6' '[- ^l !l"o" :.i,f-- !l l

4) 2sin 1'cos

5) "'

cosd = sind -

4) sins

sin(90"

738. l,

sin

I20" o

cos

1r2.=cos(cr

;cos5"

2 J"ir,o

66'1=

= cos5":

24'= -2sin(-1") sin 23'= zsin 1" sin 23";

3r srn.r, sinrgO' or =

cr) =

= 2srn{d - 60"rcosG0" =

2s" F sin 3s' - 2sin 30'cosr-s") = 2

2) cos 22"

22 zrr-n zo+L 2a-I6-1 +z< n3 -"--o--l 3"o,'* z,in tr "o"l z,y nl; ,"r,, 2 2 12 14) \ 1",,1 ln-"r f^ rul ls-urcos,, ""l " _!_"1 z"os1.oso= z.l.o"o-.o"o. er 2cos J 2---232

- sin(120'-

d + 60:) = sind

2snc-120'-dcoso 222 = sin(cr - 60').

nr,

"-ll=./2"..1 .,.

"in

4S') = J2cos(o

90'

90" +

"os

d 2sin45"costa-4s"1

45o).

o | a' 1---a zl 2 3 "t,' 2 "tr' 2 = \2 "o.ol,] t "o"n-cosdt-2 )

739. 11 2l

1) 2sin(-10') sin 26" = 2sin 10" sin 26"; 2) 2sin 20o .os 8': 3) 2cos 4d cos(_Cr) = zcos 4d cos c[;

734.

0) r(d-p} 2sinp.qso: l) 2"n{s'0t-to-0r.osrs 22 \ l^.1*ln-*l lnrol 'T * 3 2sinl"osa-2 f *"o= 5) 2"inl '-* "o"'3'" --Lol 2-232 (n (n . , )

z",n[r'"1-lr-i-1".1t

= .,6 sir

735. 11

"]'Lt-'

2t 2 Vr-"."a

va,

r",,*.,"i=r.f"'"*=

5.rcos3.[= "in5o cos5cr

= tnbo,

2sin

2cr cos

2sin2.rsin3d

cis3cr:

44'sin

2cosSc'cos.} ig!i!: 1)'2cosSqcos(-4cr) =

cos 4(x

2l - 2sin6asinr 5al sin6a 2sin50 cosOd cos6(l

J: cos25';

418

J2lJ'-sindJ =J2lsin;-si^ol=J2

;

;1""1

; ;]

sl. z,E.:,(! ' \a sl"r,lr.,. 2) \8 2/

in + al

2"i"[;

."r"f\.12 ^ "1"."f. "r.ol 2) \t2 )

".], 2)

tr I+91' ,, rl,6 zl oI r In '2 -"J r""" 6- """ ' = "i" rI2 -9l"i"l 2' '12 2) trrol"o"t n ol ,, rl@--.J=21 \2 / \ .""1 4 -""1) z zcosl\8 2/ \8 2l

2sin 45'cos13"

737. lr sin20'+cos20"=sin20" Isin70"=2sin45'.osl-25') =

= tgoct:

2 cos 45" cos 13" _=cts4be=1.

/,r crl \12 2)

zm. rr:l 1-"i"al =rr .r"n \2 ,r \ 6

30" -tsJ0.= Jj er' 2sin44'cos30' 3 236.

i) =

2sin5acos3d

=4.os\,12 2) -+-

cr.

2.os

2sj

1o 1" 6 I- * I a .r=zl\ "". 6 "". " ) = "n" 2 "o.6 2

=4cosl\R

rr)

cos25'

741' 1) (cos3d cos4d) - (cos5rl - cosorr) = 2sin9sin+ '2222

. J' ! - '8 "i' u1 ; -"o"8a = zsinn"inl-11 4 \ 8/= , 2 "'n a

"o"na

ItJ AITEEPA Mep3ncKa. r. ra iH. AxaaeMi.rHrfi piBess t:iil{ijti;i:i;:l

7a 2sin-"l sin

ttol sin

0 2\in

2sinl .222

:a::ii{liiilrii:: A'lTEEPA Mep3rsKA. r. ra t4*

9.r f.l.os

iH.

2si"*"i" i 11 9.r .os

-4sin

AKaAeMieHri piBeHb

illi

419

r d-p d 0 q+p ct-p z 2"..d--q.2"i"9.""0= z"in z - -2"".--.r=z"o"L-0 222222

2) sin 4q + sin 8(r + sin 12o = (sin 4(, + sin 12cr) + sin 8s =

2sin 8o cos 4d + 2sin 4c[ cos 4{[ = 2cos 4d(sin 8c[ + sin 4ct) = 2cos 4d . zsin 6s cos 2c[ = 4cos 2c[ cos 4s sin 60;

o; = 2sin9:!si"";0 2*" "; B-" 0 n B-d .2sincr+B 2sin ',____: cos L ' cos s+0 = sin(o.p.)sin(p_d):

(cosd -cosp)(coscr+cosB)

o - 2 sin 6c[ cos e 2cosd(sin2{+sjn60) .. '' 2cos 2d cos d - 2cos 60 cos s 2coso(cos2c + cos6c)

-. Dt

Gos;2(sin

2(sin2d + coszd) = cosSc,,)-(sino - sinss)

coJ

cos cr

";n

"in

o-lllf,f

cos

'222 u "." 9:! n

= sin(o +

Lo 222'2 "o, ' "i,', _asin.d-Pfsin,s'0n"o",*-0.l =l 2\2L)stnzl

a) cos

2 cos

r"o"

= 2coscr:

sin

2C[ . cos

= 2 cos 3q cos

-2sin4a sin(-Bq)

sin(cr

10)

zsinz 2a

2ct).2 sin 40 sin 3cr sin 4asin d

742. =

2 cos

= 2sin 0 cos q = sin 2c;

z"o"f . zsnlcoso

2*"i ["'. t1" - "'" #J ;d "." ; =

l-"9"o"o.

_4 sin 2c! cos tt = 4cts.r. sin 2q sin

*l I 2- 2"ina2"o" 2 = 2"o"9[-"g..r" 2t 2 21

t cosqt' . sin o = 2cos 9

=z"o"9l

*"9-"*l n -oll.

z"o*9

z"o,;'; ;.".;-;.i

,".] "i"'(?-rd "") **(!-'"-r") =sin,f-1-2crl \ 8 ,/-"o",11 \8 ) = = t) "*.(; - -)- *c(; *)=","(;.^) -"*,ll-ll-r"ll= \2 \8

"i,'?; =

="',(:..) ",,(T--)= =

l"in r I

t::i: anrEEPA Mep3neK A. r. ra iH. aKaaeMi,{Hnr pieexu

llilil*{l:Iri*i

cos4d =

:iilll:;:iti:i{i

ft , zol+.i,'1!I*:.'tl= rzqt. I ll I r "ini9r L8 18 * zo t.)\ "i"l18 ')

=,"*f-;)-"fl.,"l z"r"{i-z"l-"1-lJ =--

420

s) =

3.r costi tcos0 ;rr:"i,9i-0"n"9 P | 2 "i,, d - q "o" g--q - zcosd-pf"i,,g-l-p '"inor 0t;4 sin

;

sin 2d

2) 2sin2dcos(r-2srnscoso 2cosplsin20 sinar zcosc 2sin]cos3f =

,F 4q 2cos:c

=_=cls2ct:

4d 2cos4o(cos2ct-1)

2sintts c@t 2si"

PD =

nt J2cos 0 rc rl r.! r, 7t-e rcosl2 i)-2.r2cos2-"[t-;], ' 2sin2d.os2d 2cos2d(cos2cl'-sin2ql -. 1+.os4d - sin' 4q zcos'2.rl - cos40 sin4d 2sin' 2d - 2sin 20 cos2q 2sin2a(sin2d+cos20)

_ 2sin 40 cos2d - 2sin40 _ 2sin 4d(co32d - 1) _ ls4fl. _ 2d

- c fi ld 4cos2cos4.os[

... sin2s 2sin4d-sin6d {sjn2q tsin6Ct)-2sin4q ' ' ' cos 2c 2cos 4d + cos 6d (cos 2q cos 6c, - 2 cos 4a 2 cos4q co6

4sin 30;

-2sin2d sin( o) . 2 sin 2d cos

cos

I -. = t' '' 2o 2 -.4** ^i. "-* sin40cosd - cos4C,sind sind + cos30 2. sin3cx .2sin20 cos .x 8) sinAcrsinc[ 2 sin d cos c[ . sin 3(x sin o

74g. 1) cos cr

- cosdl

q"o"" = z.2.o"" " UF = sin 2d.os

2cos 3.r cos

2sin dcoE 3ct tp ar: 2.os d cos 3.r sin ncos 2.l - sin2d

B);

sin'z d + 2 sin o sin B + sin'? p + cos? c + 2 cos o cos B + cos' p = 1 = + 1 + 2(co3 q cos B + sin C[ sin P) = 2 + 2 cos(d 0) = 2(1 + cos(d

sin'd-2sindcoso rcos2s _ l+sin40 sin4a sin2d+1-1

3d(cos2ct

2sin3ct(cos2d -

B)sin(a

"o"

. (cosd- cos50) {cos2d-.os4d) 2cos30cos2cr 2cosgdcosa (sino"sin5a)-(sin2ct-sin4d) 2sin 30 cos20 - 2sin 3d cosd

"o"

0 rl-R rcos r.

zr +"rn,9:-0"in,

tj f r*":' f""" ,# : "o" l 3_ 2cr

cos2s _

2(sin2o . coe2d) 2

+ cos 2d) _ 1 + cos2a) sincr'

2C[

- 2sina(sin2s

_ 2 sin4C[

cos 222 a-0 4) (sin o sin0)(sind - sin '2222 0t = 2sin co" LLq. 2"inan0

_______:

2 sin 2cr cos

4sin

cos

--.

"i^}"i"1}.a"J

4.r

ATfEEPA MepsreK A. r. ra iH. AKaaeMiqHirr piBeHb

!t!

421

IlepeBipna:

744,l\

cos2d-zcosd = 2 cos'z

- 2cosc[ = -2coscr(1- cosa)

9: 2= 2' 2l {.1 - cosa) - sind = 2sin o - 2sin o cos a - z"ir' o l"ir' o - t2I - S ll 2 2 2 2\ 2 "i"l 2)) g J2 .r"9"i.19- ar"l= I =zsrng.zsrnr 2cosa 2sin'9

4cosasin'

2 4 2 \2 4)"..I=4 = z-8"i,9"i.[9 ' 2 \2 - +s"],l

2 \2

-zsinf

sin(-zcr)

zcosf

= 0 a6o

r -'I

= O;

o':,

or ,,6.4 0

' 2. r

x,=

sin4asrna

sin4a.

3, piBHicrh HenpaBx,rbHa. npagunbHa.

r. ,,c = :; n[-3y - 1 3y,6 = itt. (':); ."6 = .,6, pinricrr npan,r"rrna. z.t z: Jz z a Jzz: Ja v a. Btspa3r 3riBoro ra flparoro

6oKiB

Marorb aMicry, 2 se € RopeseM piBE EEE.

-3.

B) (.,e+6 .,6 ,r)'=(z 2x\'i @+6Xb-2')=4 8x+ 4x,; 5r=2t, + BO -l2x=4- 8t + 4r2:' -612 + r + 26 =0 : (-1)i 6x' - z - 26 = O; D = (-11' - 4. 6. (-26) = 1 + 624 = 625.

o<.

__l -_1r25_26_13. ' 2.6 12 6

25_,

fiepeBipr.a:

- z{s t t""z -

2.x

IIe € IcopeIIeM prB]rnr r.fi.

4\ 5)

;

hos(3d

|tcos((cr

J5,-2, r 31 2

'' =r"['*t

3J(3,r r I r3ir - 2r:

:,': :n6l r' :,rl ',r ,,6*' r* z: rx-lr'-.(J9,. -3r-2)': f +2r+1=9x'_3t- 2;8x'- 5r-3=0| D=( 5\' 4.8. ( 3)= 121; 5+ll L X" 5-11 3 JD TIi .X 2.4

422

'.:., AII|EEPA Mep3nrK A. r. ra iH. AKaAeMi'.rHr4i piBer" i:ii;ii:i:iiji::l:*

\27-

6:14 - 2\6 \2'.

2""6 = etE.

ros(3a

2c)

ts) (q

....1 .:.:nL::.

l::::i::ll

rpnrououerirvxnx OyHkqifi

- ;(cos10'+ cos20'); r 2ci)) coso r cossar

P)) + cos((d + P)+

,n 2 t( sinL 2( lr0 --l-slnl 40.1 jt"t"tup - nol *

9))) = cos29 + cos2a;

rr 3,r lsrn 5'r ',) l-sin 40 \10 -r- 40.,1 40 +

ao))=

sitr

sinroal;

]lsinza lrcosr48" ?4") cobr48'.?4"tr - 1cos26'-fcos122"=lcos26' lcosr8': "rnfup

7\ 8)

- zol - *"(([

;(cos((60'+

+ 2o)) = cos

(60'-

|"o"zo I 22222 "o"-tzo'=

BiAnosiAb:2.

Jt'

.s.E + s,E + eJ9

5") + cos(15" + 5'))

;(cos(15"

22222 z. jf"*fo

,[z-a uli.z nzl z z t-ztt 2.3-6;6=6.

<,1 /a- r

cyMy

Brpas ia nparoro 6oky Ea6yBae 13

I;;

:fq

2.6

BiA'eMsoro sfia.reHHs, piBsicrE senpaBr,urEna,

ap]' 2"1'' {2 v9 !4

,ri*tf

ITpppBipI{a:

BiAno6i0b:

z"Jz t a.lz

748. 1)

747. Hexaii ro.rarnoBa BlrAtiicrE BerocrtreAr-rcra craEoBnna r KMhoA. Ilicnn B6in6- ::::aa.!:{ IneHEs uBr.rARocri Ha 30 % Bo1la crasoBtlrL 130 %, rqo AopiBEIo€ 1,3n KM/roA. nicns sMeIImeEIIn rrB*r,ariocri Ea 20 % BoHa craEoBrrb 80 %, rlo AopiBHro€ iil:illiil 0,8 (1,3r) nM/roa. = 1,04r RMlroa. HoBa rrBraRicrE 6irblfle Bia noqarrcoBoi :da.1.O4x x = O,O4 r nM/roa., rqo craHoBnrB 4 % BiA ro.rarlroBoi flBnArlocri. BiAnogiAb: 4 Y..

6=6.

He e RopelreM piBEsHEs.

I 1 . OopMynn neperBopeHHq Ao6yrKy

Bidno6idb:7.

.3 -;

sMicry,

z+a. -s,[z -a,.,!z'.2

'd t, Js,8 7 -7' -7 -3i 4 - 4. prBsrcrb

He Ma€

BiAnoqiAb:

IepeBipria:

B'pas

)

cos(-zcr) = sinlcr srn1a = 22

rJ3 l-l=3,,i3 1+l; 1

z$. \ (u6ra,-r")'= t'-rf , s + 8x - r, = r, - 6x + st -2x, + 14x - Ot -2x(r - 7\ = O; xr

J3.1

(-"il-:,1-*"t'; -t)["."tT *] -"rT.*t)-

:r =

1.,r l;

cosSd'

d)) + cos((60'+ o) +

lcos2o

(60'- cr))

lcos60" = lcos2o

' l.

3n 1sI 33 lq ron.r' l.rl"""l r nl,"o.l n,nll l * 2 t '8 5'j '8 5') ""'lI - 40'- "." 40- "o" 40 "o" 40 z);cin(2s' 24') sin(28" + 24')) = lsin 4'+ l sin 52';

;

kos(5d -

3rr)

cos(5o + 3a)) =

cos

::::;t:::gil{l!: AIrEEPA Mep3nqKA. f. ra

iH.

"""

ao,

AkaAeMi.rHrn piBeHb

t:i:!

423

I -(; - "))J ["-[(;. ").[; - "))J = ;*"'* - ;"""; = i["."(;..) " =

!"o"zo - 1. 24

750, 1) 2.

;

60')

(cos 20" + cos

2) sino + zsinocosd

sl"a

cos

zo' = t!!; "o"

20' = cos 2g'

jGint

lx) + sin gc{) =

sinc[

cosza +

= cos2q +

751. f)

|{cosc

$n a -

z sz.

coszcr =

- cos3a)

r/.,

cos cr + cos 3cr

3o'))

cos

3d =

cos((q + 30")

cos

(c[

- 3o')))

n1 ld

fttl

tIs

1tt to

.tn\ - s,n CI = sln n = I s,nl 6 t 6.]

sin zo

ao -

slnt-sdl = sin?c/

n,tl

,r)t)=

"os

12cr =

]

(cos 2a

cos

t2 - so lltt "o"ln

= =

;

(cossct + cos 9cr)

|{cosScr

]

t-z)

"o"so

"t,,{-o) "ln

-j

(cos 3o + cos

cos 3cr + cos r

ro) =

(cos

sin4s'osd. -

cos11d) =

reperBopellss niBoi

424

r( ;lsin30'

sin

0 a\ t d rcostsin ;J = tcos 2

;.!* ArlfEEPAMep3rqK A. r. ra

d 2

iH. AKaaeMiqHnfi piBeHb

1=1

d) +;cos(2cr

2q))

cos(15" + (?5.

2d))) =

jcos(9o" 2o)=

60') -

-i"os(60" -

2cr)

"osz0l

+]cos(60' -2cr) - 1sin2cr = -sir2q.

jtcosrta

+ P)

(d - p)) + cos(d + 0) + (e B))) =

ititilliiil::::::

78")+

-f,-!*s(eo" + s0" + 2d) -; sin( 2c)f,"n2" 1sint30' . 2ot r 2c - 1cosr60'- 2at - 60' - 2ct = l sin 2a lsin

cost9o"

]

cos(so'

]cos(60'

756. I ) r 6. /f,

rpaBoi 'racrrs:

r. z"o"a snlld+rs"l-ld -2 I2l--tt ) t4 rb"ll*"inll"-rs.l-lg )t t 4 rrlll= ,l t'4 4 = cos

= sin2o +

roo = sincrsinlocr.

BnRo1raeMo roro)r(Ei

+ sin' py = 1 -r

"-i"'"'U=

- 2d + ?s')) = f,.

= sin zc +

cos'(30"

cos2a) + ;G ]0 -

+ sin(?s' =

j"i^'0 , I "o"'o - 1"in'p

I l"o"zo,l-1"."24*1-.20+rcos2n t: 22 22 2 2 z; 16+coslso' 2s)) 2c:D-lGiII(lb 2ct ;(1+cos(120"-

rrcrl =

}

i-!"^^ -i

755. 1)

"o" "i,,so,"r.'l 2f-----' I - -l z .- (sin ird - cos 7ct - cos /cl lsrnbdl 2 2 "inno"osd

753. 1)

" "i"' "t* ]1"o"'9

p) | (o -p))=

rcos'p j"."

3) cos'(45"+o)-cos'(S01-o)+;(cos(15' (75"

= I

zo *

]r"*'

|"r"'o l*"''

r 4

- jtr --"rso'" ,"rl )t - 2cr) - | rr + cos(60" 2a)) Isjn2d= '.osr60'

2o) =

sin sdi

I+zolt \2

=coF'(45"+d)

* n o ,, I * so It * I\4 . zo ttl I ---tI It4 * zo Irl - "i. ill4 -'2f'I [","11ll4r - ro r[-"llr-*] ln-ooll t)l = r] "o.[ln*ol-l'l L\4 ) t4 eolll 2[---l\a ''r'a =11

cos'o , cos'g -|rcos2p-cos2dr cos'o

-]-"

cos3cr + cos 3cr = cosq;

,fsinlt;-ul \; rzll'"i.ll , u)*t r'

"o"

zt cos'o -cos'0-1rcos(cr-p)-td- p)t cost(o

"o"60'=

+ cos3d = coso

U f, coa za - f; co" ao * j ]t-z)

30')

f,rcoallr-+

cos60o

sind-2

cos 3cr

d+1lco"lIn-ol I^, * tI * "..1r'3 Ir .l 3 -"1ll tl) 2l Lr3 ',13 "1"3 'r I 1"."2o 1l *l sin'o r cosr 2.,, , 1"".4 = * 2 2 3 "i"'o * 2 2\ "." 3l t " I . 111 lcos" d lsin'.I1- 11r lslr'(I l-cos'd--sr["c+ -=---= 2 2 22 2 4 2 4

7sa. 1r sin

sinct + sinSq =

= sin 3c[;

3) 2 jtcoso + cosao)

dl las' 33ll . ar" * " J * I ar" 3"tll .2l 4r | 4)t "'"lr,' +'t) '" 1srnd+ lf^^^dlt lotc crd 8rn 9U" | sin(1 r-cos-= Tsin cos.. =2 2 \ 2) 2 2 2 2-cos2 2 2 y peBynbrari oAepxyeMo piBEi Bnpa3r, B ,IlBii i rpaBii qacrrEax. z. 1l"nlt+s", Lr

(30' + 2a))

2o)

cos(60"

lcos(60'-

stn zo. stn no. sin ao" =

- 2o)

2cr) = sin2cr.

sin zo".

I tcos+o.

cos

120"r =

l, =,,"6flsinr-2o'r - sin60' J ,, J3 s, = n"6l -1"i"20"-1.@.'"r"ro'l aJs. 2 2 2 4 \2 ) =aJ3lsin2o""osao. rsi.zo".r.]

liliiiiiiif:iil:

I 2

srnzo' =

ATTEEPA Mep3reK A, r. ra iH. AxaAeMi.rH].ri piaeHb

tl,

425

r i 8 cos

2) Ssin10'sin50"sin70' 4 cos 80" cos 40" sin

40'

sin20'

80'

cos

40'

cos 20" sin

lepeBipKa:

20'

z"i,'9("i,'ao"

sin(so'-,r))

zsin! j + z"n]*"o

sr] r2x- lr : 6x'z- 15x ax 20 4x' 2x'-rlx 21 OiD tzt 4-2-t-21)= 121 r168 289i 3. vr'l?: .r. ll-17 22 7' *"=t' ' 2.2't' 2 IlepeBip(a: t. , = z; a. J2.7 a =2.7 +li 5.8 = 15; 1b = lb. 3) (J(3r 4x2r

,r 1r r.l I rcrrcr )l=b'4 a sln0 +sln 3d =sin 2 r2 2t sinlt2- o ) srnL )) t2 2 2 2 .ns 2nn4nn6nn sin r .os srn + cos 7 7 7 7 7 7 758. l,

3(r z

"|s.7

Bidno6idb: 7.

5r) 7 l+s,nn

761, J]iHinEa SyrKrlis

-sin1+sinn

CKnaAaeMo

2' 5'

cos15" cos25'+...

cos45'

cosS'

cos55"

75-o.

cos55"

."o"r-7-n

18r

zsrn19

\,/;=;

(r - sl'

= (.vG

L)' ; f -

=s=x

zsrn

f - 7' + to = 0;

Lr,x, = 16t

sHa.reHH.E sMiEIIoi 1:,

-1=

766.1)A=3ik=ni

2, A=:; h=7.

a=J2' 1"

y = 16 sin(S.,'

768.

21 ,!t 4x-x =r l: (JI F4,r-"r ) (jr ll':: l-4r -2t:'z + 6r =q -2r(r 3l=01r=0a6o.n 3=0;.T=3

!it: AITEEPA Mep3neK A. r. ra

iH. AKaaeMi.rHnr

.x'z x^ 2r-ri pieeau

iiilillii:i:i:*

1, piBEicrb HerpaBrn6Ha,2 He € ]{opeEeM piBnsHEs.

BiAnoqiAb:5.

426

#fl :ii:::u

I I

O,2.

npv $]/"llv ssaqelrHs oyHllqii AopiBdlo€

765.1) A = 2t k= 2'

7e;7.

x=Etb 3=u[-r; s=s.

2. r=2i 2 3=nli-1

::::i::&

t=o-

Jti:

,r^

=-Jti.

763.1)A=2,6;h=3u 2)'t=+; P=!3 764,1\A=O,6t h=2n; 2) A=Ai k = 7.

Jhi

IlepeBipnai

:::::::ii!

12. fapMoHi,{Hi Kon}rEaHHs

l8n

2sina

,i't,,J

4n srfl sin2n rsin -:ls2^ srn - 6JI " le " le-sin ""'ls =:::-!-q le ""ls' 1... sln ,-"'re =I 7r-i2

1)'

BMpa3HeMa,3Micrv.

k, + b.

3aAaHa oopMynolo y =

ll" Jnll",./e ''t 2 - o: ''r -6--0: I.r'-6=0. 1'-"3x 3 .r L3jr,0: x'0;

25'

2sin5' 2sin5' n n tr n 2sin +2sin ---- 19 cosf, l9 "o"Sn-...*2"i' "o"3n*2",n ' 2sina 19

760.

c[creMy piBEsflr, i3 ABoMa 3MiHnIIMni

762. Hyni OyE(rrii

2sin5"

2sin5' sin

OyHnrris 3aAaEa OopMynotu y = O,2t.

sin5"

2sin25"sin( 30")

;1,r.

,l-to* + t' = z.J II top+a=-2. 3b=O;5h=l.h L5k+6=1r '2 ll0k+2b=2i

sin 10" sin 5' + sin 20" sin 5' + ... + sin 50'sin

cos5"

l-il-'=,1

t li

Bidnosidb:4.

cos15" +

r/,

, i,

5+,r vtr -r- r 3 s''; l{'-r^ =r*z; 4t ,,Gr:**r*a , =-; J5 r ,r J5 '.r 'ic+t2=x'+4r+4;a=4. t 3i3 3. nepeBipra: x q;Jq- 9=Vt.4:2 J5+4

2sinI

,. ,-- i,r/'i il ,

3nr+s'n 5r ,s,nlf , rrr 3n s,nl 7 7J-sin I "'"l\ z.l

piBgicrL rretrpaB!'Irbga.

BiAno6i0b:3.

ol-lao' "ll,"i"lloo' 1l l:o'-llll I.a"i,'91 zsz. '- 2 - 2\-"inllso.. 2r L t' 2t ' 2tt) 2') iL =

f. r=O;.',4*nO d =0-1; 1= -1, z.r :; n/i-l:-a- -3 li 2-2'

sin20' 2cos80"sin80" , sin 160" I1?!l r_ sin20"= sin20' = sin20'

- 9)

- Jb - 12

,=tr"*(;-*] i:iialiilililii

1,5; h = 5.

2; 2-"i"e"-**"a'l; 'u lsllJ5 J5 / "o.,p '/5 "ine J5L

&yrlttIris

J16e

13:

rapMogiqrlor

I3l 5xl2jr)5t2 -

sino ii: r;sin; i;-";1, "os+ ,"*: rapMoHi.rsoro Ko,'Barr's.,{ = ls; ft=1.

ibyE(rris

t'=J5; h=s.

AnTEEPA Mep3reK A. r. ra iH. AKaaeMienr,li piBelrh i:.:.N 427

769. 1) a =

!rE-

2i D(d

=tli +-); E(y) = (2; +-). r i BnaqeHEs ibynKqii uicqaun: * = i[ L + 2. r: l,Ej = n z:y l=(a-z)st!-(r 2)i + 1 trpu r € [2; +-).

+2nn,neZl

fIoMiHs€Mo apr.yMeHr Brpa3rMo y.rep$

2)v=@+3)r 3; D(y) = R; E(v) = R. (y (y y ' - + 3)5 3; + 3)5 =, + 3; + 3 = {,6 + a; c - 1,8 + 3 - S, 3) v={l!. D@)=(--;0)u (0; +-}; r(y)-( -; 1) u (1; +6). t = !!J; xg=y+r;ty-a=l,aG- tt=1: y=-A npr' .r e {-€: q ! =1,1; 2t ,(y) = t2; +-); E(y) = to; +*). "=1,6 z; v-2='a !=ra +2Dp"€[0; +-). 77o.' ,5-o ' vt--"; * tt .[ br (-r t1): jr 1 Jrs t'z 23x + 121 - x + 5 =O. r'1- 23,. + 126 =Oi D = 2A'- 4'1 126=529-5O4=25i J o = s. r. =4ij =a.,^ =4-1 =s. '2',2

u (1i +*).

t.r=ta;

BidnosiAb:14.

zl liGTa+s=i{r+3t. It -t

saruisa:

tln -:l+2nn,

ez;

r = t!! + 2nr, n eZ; .. cosxa I 4l -r, Jsrccos;-+2nn,r? eZ: 5: ct cosr = piBHflHHs xopprriB He Ma.i di - = 1,04: -. cosr=;n (n <ft\ r i arccos :- r 2\n. b) n L t. = u

Ilepeaip&a:

-1; I l,ft I s- ,6 ,/14 5 2. r=9: J9-5----:=tr I = L PiBHicrh ../9 5

zzs.

cosx =

f ; t = x arccos*

2) cosr= -|; l',

( x=1Ln

{.r+3 =t.

t, 4t-5=oi ]:' _' .l r,=-t:r,=i. Itt t'z= -b

x=!

3rr

***(-1).

nt .21tn,ncZi

.l; t, *"'=-)Lr'r HetrpaBr"bEa.

zm, n

znn. n e

Z.;

r = ):!.+

t(n ^,"",.f,) t z^n.,, z;

x -;,2fln,nczl t t;\

r=ra."cosl -1?Jt znn.nezt

2nn,n e Z;

-(n -

l)_

zn,, n

. z,

+zfin.n€zi

nt *o'=

f [f = t,r' piB's's' ,.ope',iB re

Mae;

4 r=tarcaos:-2nn.neZ. a -- cosx = .-i t)

O6epBeEa BaMilla:

1.9t+3=

Z. i,6+r =S; II€peEipna:

t. x - t;

r+3= 1;r=-4; - 125i x = 122.

a+B

a.lJt+e,s i[ay.o1 .lr's: t-r.

z. x = t22i 4.{t22+3 t s

BiAnoeiAb: 4i 122,

-e .nz, s; zt =zs. ",[-tzz"

771. Hexafi Bapricrb roBapy - r rpn. nicn.s ii niABzqeHrs Ea 30 % BoHa craHoBrrb 130 %, a6o 1,3r rpE. Eicnr 3nn*cenHr Baprocri IIa 30 % BoHa craHosarr ?0 %, a6o 0,7 .(1,3r) = 0,91r ryn. Bapricrr, roBapy BMeHlnunacr Ha (r 0,91r) rpa., qo creHoBsrb 0,09 .pH., s6o Ha

95. TPl,lTOHOMETP]|qHt PtBHgHH9 I HEPTBHOCTI 1. PiaHrHHr 772. 2t

42a

cosr=b

ll cosr 223 l,* t"r""o"l .2Tn,nezi x=!f, r2nn,neZ: EI; """'=#, '=="'**Y -2ftn.nF zi x -\-2nn.nez. ::i:::AnrEEPA Mep3rrK A. f. ra iH. Ar<aaer.,ri..Hui piaexs i::i:ii:-::i:i:.:itii:ii

7z4.

-f,;

^,..o,(-r) * 2nn,,.zl 1) * znn, n e z; sx = x(n !) + znn, tr = *(n n e z; """"o" cosr,*=

B" = t

ax=+T+2nn.nez:

!' zl *.*r=*; n 12an x=x-+-,nezi

x2{

t!,,.2:

.t""""o"@ *

2n n,

ez; !x=+I+2nn,nez;

3) cos 6r =

l;6r=2nn,n.2,

'=!!,neZ;

U=!tzn,,o.z, =1*T, n.r, " s) cossr = -|; s,=t*"."(-!)*zn,o.z; al co"?=o;

='("

*** l) . 2,,.,. z:, = t([ - u"*"!) * znn,,. z, !

iiii::'...x:i:ifi::: ATrEEPA Mep3nrK A. f. ra iH- AraAeMi{Hrf piBeHb::.::::i

429

t , ", ,/:r ' Js x 3 3 3 \ 3,' 3

fil .nsl --

n 6,i 2 r 6 + arccost2 ,znn.n.z' ' = x! +[+ t x-nl=1, I, n'un ox. ',' 366362 *^=!-!=^.

77a.rt

+Z1tn.n -li "6 3

r=t3arccos@+6nn-neZ. 3

775. 1)

cos 2x =

f,;

arccos! + 2nn, n

2x =

[D'r,r + 2nn, n e Z;

cos" ' ( - rfr 1=

-E ' ,": f

f JA) =-arccosl '- )t2nn.nczi

776.

J+znr'

rl cos\n-t)

,=ti

7ao. eos3,r

,-I==I ^.,.,.

[+2""."e2;

n' 6, *- n ==u.".o"6 2nn,nczi \A rlI -J3, 2 "o"1, \ 4) 2 4 2 "osln 1=.1 ' )-!-znn-n-z, ' - 4664'2nn,n-zi' x 2 n 2nn.ncz: 3f *"[;-rJ =-r t=n z 2nn.ncz: zr

x 6,1+12-12nn,n-7,

n rxl+r=o: zcoslar "l -', ar ----\8 zcosl -"1a" "l 8' ) \

n lr - s' n :l^-".""""f] ,z^n.n.ti Jn--=larccosl a \ 2) 2)-21n.n.zt

,,-l='[^ I) ,,^.,-,, *-l=.? 2an2nfiz^n ,r

-j

8-zfin.ncz:

-g,2q+

2nn.n.z:

| *3h -t-2nn.n.zi t +3^ o-4nn,ncz. iti: AITEEPA Mep3nsKA. r. ra

ez.

1;\

1=rar.cosl -1! *2nn,n.t; 4 \ 2)

Y, 22 ar . -"--"Y

iH. AKaaeMi.{Hrr

-2nn,

n + zftn .n./ 18 3

x--:,ntBnn.n-1.

^n2nn + n. /t ;tx=1: 63

.ne/,-

Ioru =o x. = -4, r =4, la ' ra

n ,n2nllnn2nlsr. l.r I - -: 'r8318'r8318

DDX

Ja^

+ I

4a'oMr rpoMi'$Ay Hane*ar6 '.opeEi

piBEEriH"

BiAno6iAb: .{orrptr.

781.

-+' #,*'#.

" -..""."l.\2)t) "."1*+rl 2 ,- 12 \ 12l=-!, .

r. '_=-

arccos

l- t a znn. n

12 \ 2) 2n n + 2nn he/

3123

2o,.,-2, n2n! 2nn.nc7:

llDr n = ll i

2nngn2nfr7n 3 12 t2' '"' 3 12

ltnu r

2n n 312-trr=--

I I

S.n-L.

zzz.u.""([ *) =', *"[*-3) =L; 4x !=2nn,nez; qx !,2nn,ncz;,=!-,"!,^ - t; 9362 z lz*"li-sj= r: cosl; ,J. =-r1(t :a. Jz) " ,, '') 'r*^.^,t, l"=-ln "2 ,=..*""",\ 2) 2l 2 \ u,""o"fi1-::tznn,n-z; 43o

BiAno'iAb: 3n-

2rn.n.

t, ' ';-.,*-"*

cMHr.rx KoprHb

{=.1 n-u.""o"V2 I znn,n-z:' .-3J! 4 \ 2) 4 4 'znn.n-zi fipr n = O rt= -31ta 12- 3n.

n.z:

*"?= t; !=n+2nn,nez, '=!*!,".2.

t; f;2

779. cosl

,5\

"j] + znn n -z: i ln i L=xl1+zn,nez; x = +ff +:rlnn, n ez; a'c.o.

2"",

n zn I3n., =-t ,. -n366"362 =I-I-n=-I-

Ha/oubruun Br{

)T_ x=!6+^n'neLi

cos(

LIoJ1n:2 x

15n 5JI 124'3t2

2n n t4fi 39,r 13r

2\ ,:,b

t2 2n

ft t2n

2n n x-=_-

-4n

<4'I.

312 124',312 -t n7nn5nn3larl3tr <4'I: _\-?4n: _4n: - _ --<. 6126461264

31tr

t2 55n

cLb al

piaer" :lilliilllii:l:liii

iilriiitlii::ji

A'TEEPA Mep3neK A. r. ra

iH. AKaAeMi.rnr4i

piaexu

il.l,| a3r

r"..t, {1lo'..... ^.3', l3r'-5x+2>oi

r:x+2=o;D=24 4.3.z=rt JD=1;

----T\ /z:\/.-

t)l r-:l>0. \ 3/

r^=9--L=lt &r ' 2.3 3

Tr\ D(y) =lu i lu (tr + -t. L n)

2t 1" ^

3\ I

lx'

41.

sinx- b

r =(-1t'arcsinl

sinr=|; r=(

1)"arcsin|+nn,nez; t=(-t\"1+nn,nez;

E(t-.r

"in*=-121,

.=r rr,*"r'l-f.J 'rn,ncz: x=( lt^")-nn.nezt

si",=f ; x=( rY ansir !! + rv.,nez;

4) sin r = 1,5; piBEaIIIIs riopeHiB

z8o.

r) snf

4J "in

nn. n c z.

n.Z; 4rr =

,-u'

"'"",'

'=61y!+4!,,e2; 432 t :::An|EEPA Mep3reKa.

Jt +nn.nezt a{

ez;

n I -Al 2' -r-t={-1rarcsinl - )+ fin. n ezi

1=1-1fi!1!1no.o67..

s) "i'(;+r= 1, ',= a+en

i*t=

,,ez;

-X*znn,,ez; != -!-1a2nn,,.t,

, ",(#-,, =#, ",(*-#) a*-lr, = r x=t. tf

"""'".1"(-.f)

-9,

\n.nczi

sx=(-1\"^f,-

lr,

r,.^cz:

+ftn . n =7,. 'a*-I 12363

"i"[s'- ') =t; ex-{;=-!a2n ,o.z; s'=-!*#+21tn,n€z; 8x= -9! +znn, n ez; ,= i"ni,".z: ,r "'(; -.) = -1, -+ = crr. **i,(- !) * *,,,. z; f

-etri*n^.,,2t

- ctr" i * "", ". z; !

r = (-r\"'t r. ra

n ez)

zos. ry

Ee Ma€.

]' f =co"**t( L)*nn.o.z' l= t-r\"'l+,o, n.z;

r. = (-1\6n + 6nn,

6, .i.l ,-nl sinll-xl' L8 r 2'---!'' 8/

+nn, n eZ;

4t sinr = J2 {Jz - t.n:r.n ' rlr piBE'EEr Kopegis I'e Ma€. zas. r)

+ nn.

ri "t"(,-fi) =!, . [= ctr ^,csin@ +nn,n t = (-11" ! a! 1 ,n, n.7t

sinr ft; "=t-ll'a,csin fi tnn.n.z, x 't-r't^f,'nn.ncz: J;).^,.,.r, t. t.|'][-nn,nez: 2) sin.r=-+: ' (-rr"*"h[ "in*

"t-?=,+j ? = c'r"-*'[-.4)

tae.

784. 1)

= t-tti

?! = glyu L a no,,1az; x=(,11*14a!!!,n.y.

P|BHTHHq

(--; -8) u ( 8; 7l !, [2; 8) !.](8; +-). o' zJi < r; 4.r< l6i x<4i } > o. n, {a -2f," >

n, z.

loi

nn.

-rz+5x- 14=0:

BiAnosiAb: D(y, =

BiAnosiqb: D(gt =

L o 7r[r'cz.

r-.' x' "1' , .2, 2t sin{=01 \ nn,ntz: x Tnn.nczi

lx, x,= 14: (x+7\{, 2\>Oik- 8)(af 8)*0; t+8tt+ L-r

,"r. r, "rn"* = S, 2.r ( 1," arcsin !,

tr"**r( ?),n,,.2;

-arcstn

= 0; ,1 = 3; t, = -3. BiAnoeiAb: D(s) = 3; 2) u (2i 31.

lr'z+5:-1+>0.

"=L+2-!!,r.7,

a'y=f,, sinsr=-J; r"=r

ir {-11'1

"'13-xl(3 | xl>oixz-21

- r)(3 + r)

"t"1

1;5r=!+2nn,neZ;

[-r+2+0;

3) sin 5r = +y

=--l<:<RK4

Po3B'sryFMo sepiBEicrE veroaoM iErepBa"riB:

Bianosidb:

,,=fi=r,

iH. AKaaeMiqgr4fi

piaegb

iti:jtlttlit::iii

+ 20 +

lnn,

= t-tt,,'

a, +

nn, n e

:!lt!tjittt;i1: AITEEPA MepsreK A. r. ra

iH,

AKaaeMieHnt piBeHb

:-t{

43g

sin{r+ll

7e0.

1 ty"

"i, '.i=,-rf

! -!

', nn,

n=o jr=(

arcsin(

J:) ,nn.nc?: ::J

"*[,.

n.7.

,,:

r -!=(-1)!1 p16,oui6o. !!!.

npr n=

x=-:-x=-3, it"= #r"=#

"''("-,!) = ,, * ir=-X.r",.^.2, z,=-I-

*=_4!+znn,nez,,

_ff *2{,

ls*z^^.,<2,

n.z,

ttDnr=o.r '9090390-13n, rro,,=t '=.13n,2"

npr n = 2

lll

-lr zsz. rt Ja.in'*"o"' z1,z:

Jr!.",n'*

rcos' s'n1=t: 6

f,+nn,

nez: x =!

z) .Esinr .Ecos.,c=11:2;

-"'

x = (-1\'2J!

,rcs1n

*", *=;t

icos,

,, ^, srn|\2,6J=

.It -2 I

i= r t [- i-

"^. ^

,2,

434

| l, cos I , cos x sn lr ""-" -L"o"r I:' -' r"---4 4 Jt' "i", J:---Jz-

ii:: AIfEEPA Mep3Iex A. f. ra

ezi

,+f,=t tt,\*tn,

nez:

_ Hp BxoAurb y npoMirnoki

5\ ft 626 ",

sj n

iH. AKaaeMiqH]an piBeHb :::::::;i::::::::ii::i::

,,e BxoaHrL y npoMr*ox.

, rf u.."in:2 , tin,n-zi

ax= t-tf \,nn.nez:

np n=-l;=1-11' "1-4= -8. 12 ?i 12.pvn= 2 r r-1r..!-':=-!1,,=-3,x, t2 3 t2 n=- 4.x=t tl' n -1n-- I5T. t2 3 t2' ,n 2n= gn He BxonHrr, ti_.t tZ

{ l)J - t2 " -,,-l!1, ' 12, y npoMi)KoH.

Biano6i0b: rtic\h.

zgo.

eZ.

='El,'Et'

3,_,._2

1=a, 12 12 npun t.r I rr'. 'I.+t=31 =n. 12 3 t2 4'

' , *

+,h.

I r= r-lt'?I+1*Zr= -,6

nprr=0.r={

sinr-16cos"-r ,r,

2) sin-y+cosr

c,r.***f

nn,n ez:

j"r,-f *",=|, "i^,*"1--","*3 =;, "'nf" ;l l, , i=r-r, "-"r"] nn.atzi x=t-tt'n,lrnn.ncz.

ze3. r)

,=1ry$*!!,".2;

./r re .' n,?. 2 6 2,

+ 2nn, n

"",

"l ,, x.!=\.nn.ncz: "t"lr, 6 2 ' 6'

'r"-stn,

' - '; Fi

-X*

7es. sin3x =f ,

"i,,,"."1 *","r"1=i' "',(., I)=i,,-i=,1).arcsin!+nn,nez; x = ClY ! +! + nn, n <Zi 3) ssin'-+ J3cos; 3i:2J3: '.' rtrvE .i; r

n x n JeI srn2cos6 rcosrs'nd=;

*,,"

npun -t ! =r-rr -". lr= tu | 2: ,"=_+ _ "p,n= "=(-r).;-;

3i6noui6o -1J1.

",nr'.o"I6

,-I=( u.a,."ini+nn.,ez; t=gty!+!+nn,nez; ^o. "'"['-;) =], npsn=ox=1+I=1. 6 3 2' nplr n = Lr.{ t} I r:. r='ll;

rn'.

(

;.)

rr 9=@=2.,E.

J33 zr' rq_ 15.V5 _15if _.,r. v2b \y'5" i6 5 -'v" .. Bo ao Jo goV6=ovor -."' m-F G= i l2('4? J5) Lz(Jrz - v;) r, ot -- 12Jti ,5 ("rrz r"6lt,rz-us) - rz-s =vi/-v5:

ri:ri::::iiii::i: A,lfE6pA Mep3nrx A. f. ra

iH.

AKaAeMieHri piBexb ;i:::

435

r -. 16 = 16((f)' {?.r) '' itt - (vz,.J@f Vr;il = zltg zlF zj

ro(Vns =

-,F * 1) r'

ro(Jas - {,4 *

t",=*, ,=**"*+nn,nez, 9) ctg:c = 0; t=!+nn,neZ.

(J7)' *

zr (.,,6 * 2t - u({:r*u{t) = 'E) ", {/r5 - Vio -' - {a (Vs, -,6 .8 , r/2,)(Vr , Vz)

799, 1) un

r;,12.

"a1

lx.gxmors0. lt "u=l [4x x', *rqo r > 0. y = t, rpaoi& rp€Ma, sria trpoxoarIrb qepe3 roqrcn (0; 0); ( 2j 2); y = -tu + 4r, ryaoil( trapa6ona s BepmrEom

'197-

- (0; 0); (4; 0). Ia | ,axutox<-2, t.r 2) y=l ir,rlcqo-2s-rs0. lV.x.sxnox'0. 1.

y=-4,

= 4.

8OO.

0,5

ez; r=-L+nn,nez;

,neZ;

te;

7x tt tTn,ncL: - ,.. -:=43277

rinepoo.na.

4l cLg-=Oi

uo6y,cyeMo Ba aotroMororo ra6nn4i.

798. 1) tg.r

41 :_=

4fin

,nez;

2 2-nn.ncZi x=fi-2ftn.neZl

tgx= b i clgx= b

6) ctgr

ncZ: x=-!+nn.n=Z;

r = -li

n = srclg( l) + nn, n e

+ nn, n

2t cLs'

nn. n

czi

ez;, = -ff *!,,.2.

6; ?r=nn,neZ; r=4!.neZ; t; .I t;,

'6:

Sx=a."ug(-Jr) |

tgl=-w.

;=*",c[-v3{]

.-.

z: }=-!+nn,na7,

n",

iH.

AxaseMiqrrlrfi piaert

l{;{ilii::ritltl

ctc;r=b; tu|,

=It X'=*"el+nn,nez; '-|u"tsL*,n,o.7. - G .Js n n -nn.ncz: 802. 1) rcf3.r-;;J arctsrs+nn,rez: ax=')t',. f,*-i! B)

x-l .nn,nez,

h r U*=-f, *=arcwlt J:) i, I nn,nFzi r - -'d-",,,.2,

AIrEEPA Mep3reKA. r. ra

"tss"=-uj, tgsx=-/3;

x=-L+2nn,neZ;

E vJ, tg=v6; r=*"tg1,6-nn.neZ:

-1;

8O1,11 tg9a =

5; t=aJ€tg'+Tn,nezl

zt ctg.r=-u6:

436 ltl

=."6; r=arctg^'E+nn,neZ; 26=!+rn,nez;

"tgr-

16nn - arcig +;-,neZi. I;B uj,

6) c!s(-gr) =

te' vj, ' -*cl.-vJ]--,

4) tex

PiBHTHHq

= u."te (-nE) + n,,, o

O y = -t, rpa(bilr rpdMa,' - (0; poxoarrrb qepe3 ro.rKr (-2; 2); 0).

-ftn.nezi ,=[*^^,n.2,

"=***f

=;; !=*.tet,rn,n.z; x =sarcts*+vnn,nez: 3) t"[ a4)='6, t"f=-"E, !=a,.tg(-Ji)+nn,,ez;

3. flp{ r > 0 y = {,6, rpa4irc

t=-!+nn,neZ;

l) tg2r= l: 2I=arcrgl-nn.n eZ: 2x \-nn.neZ;

2. llpt -2 3 z 3

afta

Jj-,

ctgr=u[; tg

-4

rpa6ix

=f: *=-"te@*n,,,. z: x=n t nn,ncZ:

u, **r= f, Wr= nE; " 7, tex = O; x=nn,nEZ.

repertrEy

IIprt<

zt rc,

n--22+4.2=4;(2,4r. Toqrcl,l

tgr=1; x=arctg]'+nn,neZ: ,=!+nn,neZl

s) ter--a6; t = "utg( h\+"","e2; 4\ tgx-2:. x=aralg2 ^n,nczi

,,",,,' -=_L. 2a ^=___L=2, 2(1)

To.rlir r€pertrEy s Biccro Ot: -t2 + 4z - ot -r(x - 4) = oi tt = oi

c4x =."F;

^|Jx= 11

llltn _ 4-nn.neZ: x= t2' Br.nczi

i:i:lifjii:illit: AITE6PA Mep3rrKA. r. ra

iH.

Axa,qeMi.rHri piBeHb

:.{i

437

2) te(3 - 2'\ = 2i tg(zt 3\=-2r2x 2r = arctg (-2) + 3 + nn, .Z;

: = I arcte(-2)

1, 5

z; * = -

!,,.

*""(-f)

- n,,,

f;^r"tc

nels,'iJ

Jscre(s,-{J re -o:

3 = srcLe

rx = -f,

Jr:

-i

e2\ + nn' n e z: !'5

nn' n e

-L

+ nn, n e

+-.naL.. 10 5

"'-[: -;) = +, *(; :) = -,6, !-i= L--!*X*nn,n.z; ,=-n+!*znn,oez; r=

**s(-15\ *,,.,.2;

8o3.

/ tr\ ti ! + ;telr+iJ

arctsl + nn'

2) ctea-3x\=2; is(4-3r)=;; E@' s,

= - a,.teI+

3) 3te(3' Bx

+ 1)

E+ nn,

-.,6

4.,. =

zi x=

.4:) =

ez.

fir! --+\n,nELa

-;t sx-a=

arctg!+nn,ne

".2. ' -+*&e;*tt!, ".2,

o; tg(arc+r1=f; 3"+t=atc4:$+nn,nez;

ft- !.!, ".

= arctg 1 + nn, n

'lt ^ e Z, 4t=-+nn-neLi '4

16+-,neLi 4

3,r 13n nnrn=:J x= 'I + =-_ ' 16 4 t6

l7n

;;t -

Bxor!,rb y opovi)xoH.

Bidro6idb. .rorxpx HopeHi.

aos.

.i; ctsf= uJ, ,*; --Jt, i--."*( Jr)--., ELi t= n'ynn-n-Li

npun '12 2x.

:2. n. 7i

1::

Fe Bxoa,{rb

.'^'n=9 12 -

He Bxoa'rr6

y trpoM,){oKi

y rpoMixoK;

12\r2)12t24 Bidnosidb: Bo7. E

! = Ji; |

a,.ts.ls

+ nn, n e

z: ! = I

nn, n e

2! +

znn, n e

npnr, 0I

npl...n=-t x 2n z\

3 2T 4tr np, n=-2 x3

4fi

lotr

sxoAxrby npoMirltor:

,'o"n=1,=?!*2n=9!, 2n 14fi npqn=Z x=-+4n.r 2n ( 4n\ aft 6ft + l+ = =2n.

3 ! 3/

He Bxorurr, y npoMilxok:

o . 0: .r = -a a6o ugr J: or ,r arcte.,6-nn.n cz. x ntnn,nel. -3 /- n PiBHsHHs ig-r J: 0 npori*,"r Ma€ oal'n xoprnb "" - -. [u: ] Ulo6 aa"e piennnsa Ma,1o onrH xopiHb. norpi6eo. ilroO -a=Ir a I ft o'g. Bidnolidb: Eopt o=-n,o.

(r a)(te r + 1) = 0; r o=0:r=aa6otgx'l

809.

PiBET,,E' ts

BiAnosiAb: 0qrd]l.

piBH.EEHs Mano oAr-rE

438

'12 "p",.-2,=--o.-^ ,rrJI5JI +-=-. nDlIr=l '12212 r=

fi- He BxoA rb y npoMi)*ox: npvn=0r npttn=1t= n+3n=2fi: Rpvn-2x= tr I6'I=5,I He BxoA[rB y EpoMi]HoR. 806. crg2:r=-./!;

8o8. {x + d)(Lg.r - J3) or r

'16416

np{n 4x--:

Li t

BiAnoeiAb: 2it.

."rr=O r=3, ' 16 nnEt f,nu n=l x= +-= nnvn=2 r=-+ '1621ti

snn, n

- ! - t + nn, n ez.'

804. te

f,+

t nn, n -

n=o x=-12i -fin7fi '12212

5x =

npu

n e z.

uslrx'li=

-7t= 2x

tsz'=-f ; ,"=^,.@( @)*no,n.z,

i::J AIIEEPA MepsnqK A. r. ra iH. AKaaeMiq{lir piBeHb

+1=o

Bionoliab: rrp*t

1g.r '1; t=-!-nn.n.2.

"" "n"*,**" [- ],

nopilr6, trorpi6Ho, qo6

Ma€ oar-{E

Rop1ts6 --. t[ob,4axe 4

n 4

"= !;"< !;">0.

i:i:::r:li:it{lillj ATTEEPA Mep3rrK a. r. ra

iH. AKaaeMi.{HrF piBeHh

t:i:l

439

'l A1O. trIo6 rpaoi& OyHriaii 6l'8 ctrMerpr.rqElri siaHocEo oci &oopaltlrar' OvlrHqin no BI{HIIA 6YTII trAPHOIO. I

81s.

OyE&qis trapsa, ryaabirc cr.IMerplrqHri BiAHocBo oci Oy.

sin(-.r) r i l-cos.r ll-x)=:=I lcG(-.r)

l-cos.r

<DyrIKrIrs Eeraptra, ryaoirc Ee cvMerpn'rE ii Bianocso oci Oy. + lz + + d2 + = st t@) = tt-'> = (DyHFirIis rapEa, rpaoiK caMerplrqHr'ri BiAEocEo oci Oy.

dr-

4) f(x) = x' \E x'

x) =

E-t-"l

(-t)' ts(-x\ = -x'

i \Ei

+ tE -

2\ ait

Hi;

4) rarc;

si;

5) Ei;

ti)'3\3,r l -- l= --. -"/n\

8) raft;

9) ra&;

9a+1=r. rar: tr !!."-! ="!L . "i 43 \2 44 13) arcts(-1) = -:, si; 14) rax; 813. 1) I{e icEye, si;

8) arccos 1 =

10) ralc;

11) raIi;

12) arctg

1t n 5r, ra);+6=-.ra1c;

15) rax.

814. 1)

a) cre(2 =

0' Hii

= 0, IIi;

817. 1)

"o"],u.""o" \ 3

1l. lr 3,/ 3 2ta:

4* 4:: |

4 \

tr: 4

I 2

4) n.

rr+-+ fi-+ 2 3 t

3n+6rt+2rt+6fi-n

16?!

8'r

663 6n+3n-3fi+ 4n-r 14n 7n 12 12A

-1< Ji <t; 0 < r < 1; ,(y) = [0; 1]; 5t D(y) = Ri 6) x / 5: D(y) = (--: -5) u ( 5i -)i

7lx 2>0ix>-2:D(gl L2t *)l

("-f

="1"101

=".,un

""[r^

])=

.11= _;:Jt crge

l$: AITEEPA Mep3nrKa. r. ra iE. AKaaeMi'{Hr'rr pieens

.1.,

[-'' S) I--x-"

ir> l;D(?)=[1; +-).

lr-1>o; A21, Ir -1 < x + 2 <

-g

z) rs:<L 3x2x2r-:=

rr' "i.ls.I-1ll nr=-r, | \ 3/./ = "r"r I / nl n) I r\' !5 6) telz L--l I - tcl-6I - t: 6.J

440

eto.

n' I 7t 'r I -"o"1,,,, , r-51=coslz'I s.] =*"5=z'

2,) ".""."111

=ot

(n-a"ccteJtf)="*lt

"o"lr.n,l" \ r \

6 46 4 sft 4\ 10,I-lon-l2n zt zln-!1. s.1*n.l-I)=2.sft -'-1" 6J -3'\.2t-'e e-T= a-=-2" A2O. l\ I < t - 2 < 1; 1 < r < 3; D(y) = [1i 3l; 2t -1<,'- 10<1; 9<',<11; B<:l<."{J; lfvl = l-Jii; - s] u [s; "/i1]; rr t'f sr, -2s1<2t r< -j'u.'= |,og1=y*r-Lp1f,, a,

9) se icEye, si;

*"(;9=+'

619. 11 -I..s14-,1=I'

cic; = L

-"[,;J

cosl

zr!2

7) arccosO = I. si: 2

ri;

Ilr:

3) ra(; 6) ran;

Iz$i

n-11+lll="".r= 3 3,/

r .3r _.13n 3 4 t2'""-r

5) ran;

13)

/2.1_\l= .".1

818. 1)

4) raK;

0 = 0;

cosl

t2l arccts0=I.si: '2 15)

"i.1=@, 32

3) raK;

lO)

" 4/ -cih_=4

5) ts(2'i) = b;

811.1\f(t)=f + 3i t e IOt +4i t = g' + 4; a" = * 4' u=$ a trprre [4; +-); 1;U'=x+1t A= Jx+1, t€[ 1;+-); 2\flxl- 'z-1;t€(-;Olit=A' s\ f(r')={V; re( -;ol; a="\Ft u= vF, re l0; +-). 4. Oyxxr{ii y = arccos x; y= arcsin x' y = arctg x; y = arcctg x 1)

= I 4,] 2 ar -\ t'l = cts4 o: "tn[z 4,r -2 =

(Dys&qis EenapEa, rpaoil{ He csMerpt{qHsfi BiAHocEo oqi Oy.

812.

sin.t

sin

q-x' 4-x' 4-l x)' I /(r) cost: rl" ir' = cos(2 ( .rJJ cos2.r'

2J ' l{})-,

trl -sm_=sintn_ . (n 3r -, /l srllt -+2,^

r < -1;

D(y) =

3; -11;

:, Dtvt=(-,-:),'l:.'-J,

3) -1s J.! < 1; 0 <, < 1; D(y) = t0; 1l; 4, x 3>0; t>3: D(y) = [3; +-);

llillilif.il{!:l

::i*iir::itttil: A'TEEPA Mep3ncKA. r. ra ifl. AKaAeMiqHr,rfi

piBeHb

li.l

44.1

fl 5) D(v\ = R;

x+7+O;t+ 7;D(V)=(-; -7)u(

I' x-1-r. lo-1=r.,,r,

lx>0i

l.r>o:

2t l:lxttl

7i +-)i

O6epEeHa

to,,r.

L=5. 3r,i,u. ?I I T 4'rx .4.2x+7 [r' -si ++=0, ]l = r, r, =a. lr+0, lt*0.

r) -]<u."si,'' <!; o < ",.'i"t +! <'I; v.,^ = 0; v^,., = 7.; 2) 0. arccosr. n:2sarccos.r+ 2<n t 2iy... 2i 9,,," fi- 2i g) -1<u.""i,'r<;; n<2 arcsinrsn; 3=n-3t "-I<z**r' 4nn2fi4n2n --i.zu'."int t's,s", -T: ,"^ = a, 111t 4t 0 arccos x'n, = ur."o"r n, Y- n. z\

',=

rr fi 'r 6i 9"." 6. C",.

19r

< u'""in'<X;

-L

< u'csin"

4j] =t; z'+1=rr"= tx 2x + 1= 4xt 2t= 1;x=O,5.

= |-zt

3 arccos

a24.1)

,r r

o-,"=X,

,, =\+2.

.E;: u.,, =0i v,' ="r" ,E; zt ')',*'t,*: ir 0t Jarcsirx:ll' a.csin G j 4; v",'= 4: ,, 82s. 1) \t>0; o<u.""i,''4<l; +4<

21 0

sr6. r)

=L+4.

zr tel**nJ)

/(-5)=( 5,16 0:g(21=2" Oigtl)=l:g( t) 1. et I ): E{l ti /(2)r /{ 5,, 830. CrnaB Macob 36 rr uicrrrr 45 % Miai, rqo craHoB'rb 36 . 0,45 = 16,2 Kr. flIc4o Ao Irboro crnaBy AoAars r Kr MiAi, ro iroro Maca cranoBmb (36 + r) !tr, a MiAi B nr,o, My 60 %, qo craRoBnrb 0,6(36 + ,) Ir.. CKna{a€Mo piBHnEEs: 0,6(36 + r:l=16,2+ t;21,6 +0,6t=16,2+ tcr 0,6 t - r=16,2 21,6i -0,4x = 5,4: r = 13,5. llr

831. 1) SaMiHa: sin

(

t2\

2) cts "t arccos-

t3)

ztz +

t- I=

Oi D = 1

13 JD s; r,=-l-q 2.2 r, r"= 2.2 siri

O6epHeHa 3aMiEa:

",,. ', "*(***])

MiAi.

5. TplroHoMerplr.+ri piexiurr, r<i aaoAirbcr Ao anre6pai'qHl4x

1% E'' 1J15

""=

t+3.6

829.

Btdtlo6,ab: 13,5

pe.

*"[***;)=

=4,

Bidno6idb:

' o, O sl6.cco"r: Jn.

arccos,r

1-3.6 22

2; v,",= 2:

yt2"'1

{j*=0,

4) r'+x-2 {x' t-2=8 z. gr-1"", G' *-z = t. t, - t - 6 = o: t1 = -2; t, = zO6epEeEe 3aMina: r[S *t-Z=-Z; ftopeuiB HeMa€; .,8 *t-Z=Z; x2+r-Z=g; tr:.lt ,,+ ,-11=o;D=1 4.(-1.1r=45: Jo =a,,E: ,,= t-:n,

J;>o; o<arccos,4<|; z<arccosG+z<]+

,*1-s=0,

Bidno6idb: It O,5.

n; y,,^,= 2n; s-,,

o6ep'e'a seMiHa:

3) 0 < arccos, < 7t; 0 < 3 arccos ,. < 3fi;

;

Sar,aiHa:

r = 252. BiAno6iAb:252.

ezz.

823. 1)0sarccosJ.<rx; n < erccos r. + t! < 2n;

(G+a t.t?tBt .28 Ot!t=.7.t2.4. - &opeIIiB HeMae; \li+4=4; x+ 4=286t

-3V,rr4 =28. saMiEa: {rtS=-l

r = -1;

- 4. 2 ( l\

= 9:

x,-'tn1t2nk-htz:: "i"' j, "=r-rr,X ", ,"t. BiAnoliAb: C1)'! + nn, n eZ; -! + 2nh, k eZ.

F;G;r lIH =

2) SaMiHa: cos a = t. 2t,

D 25-4.2.( 3t

- 5t

25 F 24=49:

JD t, t,=5rtl a, r,=!r.l

)

O6€pIIeIIa saMiEa: cos a = 3, (opeHiB EeMa€;

10 = 0. SaMiHa: ts = t. t2 - 3t O6eptr€lra 3aMiga: f =5a6ox3= 2; x,=lli;

A2a. 1) 16 3r3

20 = 0; t1= 5i

t,=

Bidnoaidt:

,"=<l Z=-:12'

i::l: AITEEPA Mep3neK A. r- ra iH. AxaaeMi'{Hhr pieenr

t.l ., r -fr t2nn.n \ r,..." 2) 2nn.n-zt x. !2n 3

iiiiii{lilllii:

t. t, + 2t

3 = O: tt= 3; t,= L = 3, KopeHiB H€Ma€j sin 3, = 1: UresPA Mep3rrx A. r. ra iH. AKaaeMi.rnri =

O6epHeHa 3aMina:

lil:iiii::iili:iiii

7..

+2nn. n eZ.

3) SaNriEai sin

Bdno1idh: !2i \6.

442

2 "o""=-.1,

sin 3r

piBeHb

,:t

44s

Bi.lnoaial6:

= arctg

(-1) +

'rt,

r he Zi t=-I+nk,heZ. fr

flh, n, h'2. -4 + fini 5) 3a{ina: ctg 2t= r. 3t' + t - 4 = Oi D = t - 4.3. (-4): 4e; uO =tt t,=-j|

Bidnolnb:

-!t

-l +7

O6epEeHa 3aMiBa:

lsfln -4 2 2^.cts-+-.neLi

433-;i tgzx=-=i 2x = - arcLg i t nn, n c Zi cLg 2x = li lg 2x = li 2t = arctg 1 + |th, h e Zl 7fi,th +-,h€L, a= fi nh x= a+r,REa. l3rrztrft[ :-; , n, h e zBidnosidb: ;arcLc;+ ;t ;6) SaMiEa: cos I = l. }t'z + 5t - 2 = Oi 4 cte2x =

=2i - 4.s.{-i)=4s: 1o =t,

O6eDAeHa

t,=fi .

Bianoaiaa:

-5+7

2.4 -'

Bt,

-t-

"l*

nu, u

ez.

ah, n, k

2 = Ot D = 1

4 . A . (-2,

Zb;

ts;

-;; ; = -*"t sf,

n*. * e

z: r = -t *cLcf,+

''-h.

+ Snni -Barctg! + Bnh, n, h eZ.

1)sior- cosr=0l:

cos

r; tg.r 1=O;tgr=l;

r=!+nn,neZ;

2) Jfein++cos.r=ol:cos:; Jttg"r+r=0,

tc"=-;br x = _!+nn,nez; 3) 3 sin r= 2cos.rl: coatiatgt=2; tet=!; t=*.tef,+xn,nez; 4) Acos2x-sin2r= 0i:cos2.t; 4 tg2x=OrtE2r=4:

am, n ez.

ez.

2.=a:(jts4+ftn,nez; l.= I*ctea+T, n ez; 5) sin;+5cos;=01:cosf; tef +r=o; tei= ^s; i=-*"teb+nn,nez; t=-3arclg5+1i.n,neZ; 6) sin'?.r - 5sin.t cos r + 4cos? r = 0 | : cos2.ri tg2 r - 5tg, + 4 = O. SaMisa: tg.r t.t,-it t 4=Oi fr , l:r,=4.

o6ep*esa 3aMiaa:

1-7 3 \= tt = -i'

1+7

= 1i

-*cttl+

nn;

ctg{=1.

"*i = -?'

834.

sin't - 3 sin t + 1= 0.3aMiEa: sin, = t.2t'z'3t + 1=Oi D = s - 4. 2. t = 1; ln =1; r, =f;j =t r,=T: =i

832. r)

=7;

glclqo IlptrIryc"rrr, qo cos , = O, ro sin , = O, - oAEopiABi. oAFoqacEo rli ABi piBHocTi se Morri]"r,r, BrrxoEyBarrrcs, ocrcirbrin cog2 , + sins , = I, ToMy cos .r * 0.

-z;

t**osl+znn, nez; r = +4zrctoe!+

arccoaf, + 8nn, n

833. Aerlri rrir piBBrsE

3aMilta: cosl = 2, xopesie uemae; =

l-l!=1. ? JD=s; t,. ' 2.3 ,,' =r-5 2.3, 3. O6epEena saMiria: ctEl = t, 1=O*nn,neZ; r=4+Bnn,neZ; Bi}noarlo:

-"f=|, i

X+

4) Sauina:

z=!+nn,neZ; tgr = -9; r = -arct

2t - 3 = 0', t1= 3i t2= -1. = 3; t = arctg 3 + fln, n e Z; tg x = 1;

Bi()nosidb: arct! 3

O6epEer€ rar.iEa: tg

4) SaMiHaftgr=r. t' tg

-t-

= r. 4t,

D=1-4.4-(-r)=as;

:+-.nez.

O6epneEa saMiHai

3) SaMiHa: tg

fi zftn 3x=:+zfin,n(Zi x= 6. 3:,ncZ.

sint=l; x=!+2nn,n.rt "tr t =f,,

O6epEeEa BaMiEa:

Biatuolilb

2nni

n, k e

[ nk, | =O; 2) BardiBa: cos 2.x = t. 2t''t D-1 4 2 (-t)=9: JD=3; 1,=L1!=1; ,,=;;= ; O6epEesA 3aMiEa: cos 21 = lt 2t = zfin, n e Zi x = fin, n e Zi """2' = r = tL

-tt

+ nh.

Bianosilb:

444

F1)'

2r=rarccos(

1)-z*.*.2,

!;+

li r

= srctg

+ nn, n e Z:

tg z = 4; x = arclg 4 + ith, k e Z.

Bilnoaidt !nn: ?) sin,

2x=x?+znk,nez;

heZ.

;

Saruira:

arctg 4 + Itk, n, h

I+

nn, n

eZ;

e Z,

! * z*." = o;l** i i, E ; tgf, = r. *-Bt+2=Oit1=2it,=t. - ssin;cos

;

+ 2 = o.

O6epEeHa BaMiEa:

ftk, n, h eZ.

l:::l MTEEPA Mep3rr|( A. r. ra iH. AKaAeMi,{H'i piBeHb

ii:i!#idlllii

tt i

nn, n e

n71,

j:i:lttilJii::ti: ATTEEPA MepsrrKA. r. ra

iH.

AKaAe&ti.{Hri piBerb

^r.tc

+ 2nn, n e

rt:j

445

E;=2t t= Bi(Jnosdb:

;+2\nt

8) 3 sin'.2 BaNriHai

arcrez+ nk, k 2arcts

sin, + cos.I = 0

cos2

2flk'

cos"

+nn'

: cos

2\ 2(l -cos'r)+ 7 cos t + 2=O;2 2 cosz r + 7 cos r + 2 =0; -2cos'zr+Tcosir+4=0. SaMina: cos , = t. 2t, + 7t + 4 = O I I C1\; 2t, - 7t - 4 = O; D=t-lt:-4 2.{-4,=8lr vD 9: / t^'.n *' ,. t.+=-1

= zarctg 2 + 2nh' k e z'

zJat+1'=oi

ts'=f; r=*""tsf 834. 1)

216 sin r cos, +

ts,=t. 3f

ezi t

- z'

o=(

x; \te' x -

zJa)"

nez, x =I+

z^13 Lg

+ 1 = O'

2h -t a-t=o; - 23

O6epHeHa saMiHa: cos

+ nn' n eZ;

?!-2nn.n,r. \ ^ ***'l 2) ,^,., z,,= 3

-1; t ='!

2.2

ftopeEiB neMa€;

Bidnosidi: !2n t 2nn- n - /

nn,n ez

r; tg, + 1 = 0; tg'

t, 2 *

"E 3

r = 4;

3) 2cos' jf- 1- 1 - 4 cos r = 0; 2 cos' r - 4 cos x 2=O. SaMiHa: cosr= t.2t, - 4t - 2=O .2; t, 2t 1=Ot D,={ 1f - 2.(-t\=2: t; t;.. ,, t;-. , t; O6epEeHa saMina:

2) sinr.-

cos"r 0:cosx: ter-J3 '0: tsx J3: '

i' "^''-z'

0l: cos t;2tg Jr + 1= 0; r1 lgx=-.i x= arctg +nn,neLi 4) cos 4jr 3sin 4' = 0 | : cos 4r; 1 9Lg 4' = Oi I1-tlnn tgar i: 4x=arctgl- nn.n-Zi x Aarctg B1 4'nFLi 5) sin':r - 5si.n r cosJ. + 6cos'r=01: cos',; tg2 ,. 5 tg' + 6=0' SaMiHa: tg, = t. t2 5t+6=Oitr=2"\=3.

3) 2 sin ir + cos, =

O6epHeHa 3aMiHa:

= 2t t = arctg 2 + nn, n e Z; = 3:.r-ar.tg 3 - nh- k - Z. 3 + nh' k e Z" 2 + nn, n e 4 BiAnosiOb: ^rctl ^rcte 3 sin .r cos :c - cosr :r = 0 | : cost4tg'2t-3tgt 6) 4sin'::s-

te lg

l. 4i' - 3i -l 0r D - (-3)', 4. 4. (-\) = 25i,1O = S; t, =?E

1=O'

- 3 5 _! "

2.4-

O6epEeHa aaMiHa:

tgx=7; t =\+ nn, n ez; 11 tgx= : .r = -arctei+ nR. n e L. .1 " -F arcLc;- nh. n' k - Z Bidnostdb:

cos't + 5sj.nx-7 =O;6(1 sin'zjl:) + 5 sin t - ?= 0; sin't + 5 sin jr ?= 0; -6 sin'n + 5 sin '=0 1=1: Sauinar sin;c=t. -6t'1+5t- 1=0J: (-1); 6t' - 5t + 1 = 0; D = 5' - 4 6 I I 5 5+1 r il- z.t Z, t ZG t' JD.l:

835. 6

1) 6

O6epllena saMiHa:

.r." = 1, r=r tt'L+nn,n.z; 2ti

11 (-Irlarcsin nk AFl' i: .t I Bidnfiidb: /-7l'!t6',T,?: l-1) arcsLn J t n*-n-k-7 446 li* AnrE6PA Mep3neKA. f. ia iH. AKaAeMi{H,r pieexr i:::iliii:ii::l:i:ili 'inx

! arccos(l Jz)tznn., -2. 2cosr (2cos'zn- 1) cos,r=0; 2 cos, 2cos,.r+ 1-coszr=0; -3cos'zr+2cosr+1=O. SaMiHa: cos r= t. 3t'+2t+1=01:( 1);3t, 2t-1=O; D=t tl 4.3.r tr 4 rt2 t6i VD 4i i 2rtl t , Bionosidb:

3aviua: cos x lr .:r htn. n - Zl !, ,-,( , a.ccosl'l +:n*.ecz. 3 3) \ Btdnosdb: 2nn, -r^ 21*, n, h * L. 3l \ "...."1.l 5) (1 2sin' jr)+sinr=0; 2sin,r.+sinr+ 1=0. SaMiHa: sin ir= t. 2t'+ t ).1=01i( \)t 2t, - t - 1=0; r-3 ,6=:, t.=1-3-t' ,^ ' 2.2 ' 22 -1. 2 O6FpHpHa

t r

Sevinai 1g x =

1+.8; nopesiB HeMae (r +.8 t r); cosr = 1 nD; x=x.arccos(t-nE)+znn,nez. cos rc

D=1

- 4.2. ( l)=9;

O6epEeHa BaMiHa:

stnx=

li x= n,+zfin,n€Li

l, a=t 1tt't!+nk-kF7. 26 Bidnoaioa: L+2nn: t-It"'\ - nk.n.k.L. 26 er'333 z.o"'{-r-r"n"1-2=0. BrMiE': 21:- 5i,3=61 "."1=1, 5 7 I D-l5F 4 2-\3).49:.JD 7: t 5'7 22 t' " 22'"'" .inr=

ooepHeHa 3aMiHa:

cos{ = 3r xop.r:le '"'o,;

1, ,--"tl',',., 3 2 "3 -l\ " 2) r=!2n+6nn-neZRiAnoqiAb: X2fin

ez, x -2^ znn.o-2. 3 3

+ 6fin, L e Z.

i;i:::::ilLiilti: AITEEPA Mep3rel(A. r. ra ifl. AKaAeMi{Hr.ri piBel/.b;i,:.:i 447

r = 0. SaMiEs: sin.t= r, ',t'-\f2t=oj - sin'

:r:

- rE

O6epEena BaMiHa:

\Esinir=0:

l-2srn-'r-l'sin/x

7) 1 2sin x {l-sin'rl-J2sin'r=0r

rg5x

sin

ru"rn!-!!.p.r. rs5r=9: sr ante3 "4 , nh.kczt ' 5 '4 i 4 nh -finnl _+: . afcle 3-|_,n,k€z. Eidnoaidb: 20 5 5 -4 s 12, 7 + ctg'z t = cte t + 3t ctg, a ctgr-2=0. SaMiEa: cte r = r, t, - t - 2 = Ot t1 = 2, t,= -1.

t(l+.€)=o; tl=oa6o t,=-Jt

O6epEeEa saMilra:

sitrl',=O:t=nn,neZi sinr = .E; rcopeEiB EeMae. BiA

o6iAb: nn. n

e Z.

?--\

-"j ' [z*"'j -

3auisa: cos{=r,

2t2

D=l -4.2

z*"'i

-"i

O6epHeFra saMisai

-r

= o.

t,= arcctg 2 + nn, n e -li ctgjr *=-!+nh.*-t. clg x = 2i

1=O;

I l'3 - 3i \= r-3 = t. t,- 2.2' 2. VD 22

f-I).9i

Bilnoailb: arcclg 2 + nn; -!

rr1 2"i1': . cos- J

O6epH€ra 3aaliEa:

r-=n t2ftn,nFZ; x=2n -Ann,ncZi

22 "o"{=.1:

.".;" i, ;= -l-zn*'*.2, x

BiAno\idb:

ft.-Y.nEZ:

l:5x=Inn, n-Z: x

Acos,

+ nh, n, k e Z.

2-llcos'rt -7 o; co-+4cos-x

srtz=o' t.?-2t,tr z=g.2-2t-tl-zt =o. [er" t t li*o: D ( st .4.4.2=4si lo z, r,=Lz.l ,, ,,=\+=l

aaMiss: cos,.r =

a+ t ank.hez.

i++ 4rki 2n+Ann.nez.

O6epEeHa BaMisa:

cosz

1fikJ-2i !t-. 9) ter-\gx

saMisa:te,=1.

t+!+z=0; t'+?t+1 -0.

O6epdeHa 3aMiEa:

I:':;'.t=''

(,r1)z=0;

2: .osr = -!f2 a6o cosx =.Et kopesis

l, "" *2!,2,,,., 4' "o"*=-1.'oo 2 --' --'^ "o"'=1, 2' '^ a6o t=rI+2nh,heZ. Ilicnn

o6'eAHaEHs ABox cepi:fr ftop€HiB oAep[ryemo

Bidnosidb:

t')

14)

r - 1 - 4/icosr

2 cos'

+4 =

2coe' x

SaMiHa:cos'=r. 2t'- EJ2t+B=o; o

, "= zz O6epEena BaMiHa: -) cos.r=s.[2 i kopenrs neMac la,6>]J:

&opesin Her'{ae;

arc.orf, + zn,

aJr-2J2

o. z;

6x =

+ 2nn, n e Z;

ftnn t=+-+--neL. 183 Bilnoeiaa:

Bi'noiiAb:

tg5,r=

a 4t-7t'3 t,4t +=-7 O,- ,-

D r7l, 4.4.s-l:.lD=t, 448

t, =.7r+r1

=rr

- l4!" n+a uilr*0,

eZ.

- 4rE

(t,lz)' -

cos x + 3

= 0,

+. z . a =

J-o =znE;

2,2 .tE 2.2 =T'

aJ2

| 2

t;.osr = ;: x-,".2nn.ncz.

nez.

'7=0t 5x*T.ncz, * 'ff.r'z Irt 4tesx+-9 tsbx 3aMiHa:

BJ2 z"'=

!{j+!,

+ nn, n

t nn. n c z.

*"6t

cos 6r =

O6epEeEa satrfiEa:

-;;

HeMac:

--- '"os'x=

t = 1i x=-:+fin,neZ.

cos,6x)-5=0r 4cos,6jr -4 cos6.r'3 16, g.1---j919{,41t 2 SaMiEa: cos 6.' = t. 4tt + 4t - 3 = Oj -4+8 D - 4, - 4.4. (-3)= 64;,!o = a; t, --j:3 = -?' 2.4 2' "' 2-4 =

/=0'

+ 2fin, n

eZ.

r + 1= 0;4(1 -cos,r)+8cosr+ 1= 0; r + 1=0; -4 cos, r + 8 cos, + 5= 0; 4cos'z,q 8cosr-5=0. SaMina: cosr= t. 4t, 8t - 5=0i

836. 1) 4sin,Jc + 8cos

,"=?; i

!!{j AITEEPA Mep3ntK A. r. ra iH. AxaaeMi'rHlli piBeHb iillia:.:tiilllN

4cos,r+

8cos

ii1:itii:::lillil: ATTEEPA Mep3nrKA. f. ra l5

yci

rtq

u., !.

iH. AKaAeMi{Hran

piaeau

!il: 449

D=r-8) 4 .4 b

t44i

06epseEa saMiEa: cos r = 2,5; KopeHiB HeMae;

cos

| -r ' - t; jf +| n -

Bianoaidb:

arccos

+2ILn. n

tz,

a-.12-2.s,

l\ I 2",-n.2, ' 2.J

, =";Y=

sin; = 0; -2sin' sin; ;+ 3ar',rina: sinl=t. 2t'z t 1=Oi 6) 1 - 2sln' ;

D=r 4.2.(

znn.r-2.

=4s

€2.

'^ ;

26 3) 1- zsin'.T + 8sin n 3 =0; 2siD't + 8sin t-2=Olt(

sin'zr-4sinr+1=0. SaMina: sin, = t. t' - 4t + 1 = O; a D = 16 4 = 12: .lD 2J3t t,

2);

2 SsinI l,\' -"ll ---31' 2 0; 5sin 1-5r """6 6 6 2sin'1sawisa: sin{ = t. 2t'z+5t +2=Ol 6 5.-r3

= z, t.=-f,tr3 ='t.

2'th- n, k

Scos

2 = 0.

,=#= ;.

tl+!,

ter+-L

n)tzon.nez: 4x -2n 2nn.neLt

ez.

a=0. 1.

2 t'!-3t+2 3 0: l, t t

O6epHena BaMiEai

ll gt2=o. 0F ), Ltlo:

l.=2il-=1.

tg x = 2;, = arctg 2 + nn, n e Z;

tax=l: x=L+nk,keZ. ft nk,n,hFL. Bidnoaidb: arcls "42 ' nn. 9) \6tg'+3=3(1+ts"x); \lite" saMisa: ts

r '6ter=0.

' = t. 3l - rf3t = 0i .far(J-:t-r)=o; r-ouoo ,=+=@ J33

O6epHeHa saMiHa:

lgr=Oix=nn,n.Z;

xooesls rreMae:

.t"* -1. ' 6266

-f^

O6epHetla BaMiEa:

I z: "in 6 =

HeMac:

cos4.r

SaMirla: tg jr =

n.heZ.

D=5, 4.2 2 st,[D s; t,=

sarilla; ros 4.r = 2i HoppniB

Bianoaioa:

*.6 t r);

=2-.,6; r = ( r)"arcsin(z-16\ + nn, n ez. .2. Bianoliab: etl. arcEi"(z - nE) + "", " a) (2cos'9, 1)+(1 cos' x) - cos t = 0; 2co]' x - I + 1-cos2?-cost=0j cos'r cos r= 0; cos t(cos t - 1) =0; cos r = 0, a6o cos t - 1= o; r =! +nn, neZ ' a6o x = 2Th, he z' 2nki

- ann: t-:.f 'i|-

},.x=+!+\.nez. 63

?fi z*h, t.=z $

sinr

O6epseEa

-2

O6epqeHa raMiHa:

\+n

= 0.

D=(-st, 4.2.2=25,5=s; t,=f;j=zt

1 ll' \ -2nh, n,k'-Z-

..ope'iB EeMae (z

t, |

7) 2cosz 4' e.1*?"4'*r=o; 2cos'4t 3 Scos 4ir + 1 = 0; 2cos'4r 3aMiH€: cos 4r '. t,2t: 3t 2 0|

srnr= 1: -r= \+2nn,neZ:

Bidnosiab:

t,=!j=ttr=i:=

t: |=!t2"", n.zt '=n+4nn,nez; == t-tl' t nn, n. z, r - (-:rrhi ! + 2nh, k e z.

Bidnoiidb: n

06epnesa saMiHai

sin:r=2+16;

5=e:

0; 2sin'; - sin; -

"t"|=

2(1 sin'j9) 1 sinr=0; 2-2sir\2x- 1 sint=0; -2 sin'? r - sin , + 1 = 0 I : ( 1);2sin'9t+sint 1=0 SaMiHa: sin r = t. 2t'z + t - I = Ot D=r, 4 2.{-1) 9i Jb.s: t.= )-r"=-t, ,,'}.trt

n,21t 26

1)=e;

+1=

O6epEesa 3aMiEa:

Bidnoeiot:

r rf 'L

tgx = !9; x=1+n&,keZ.

nn,nez; x=( 1)' n.6nn.nrz-

Bianoliab: nnt

Bi0no6iAb: Gl\"'tn+ 6nn, n eZ.

450 lii: AIrEEPA Mep3reKA.

f. ra

iH. AKaAeMi'{Hlafi piBeHb :::a:::::i:::::i:i$:i

[

+ n*, n,

* e z.

ljll::li::tlii*: AITEEPA Mep3re( A. r. ra l5*

iH.

AKaaeMi,{Hrr piBeHb

ili:

451

ror n"in''

rl -u=0, \ -1$n-.r - )

* g{

4 sina

- 9sin', -

6 sin'?

D=2, 4.b.( 3)-64: Ja=6; 1,=-?:!=-l: r.' -l+-q=q 2.5 2.5 5

=o-

O6epHeEa BaMiEe:

9=0' t. 4/--15r'9 u- o l4l'-15i * O, lt -r5-9 15-9 =u, t,=D 15,.4.4.9 8l:JD=9i,,':.n

ts-4x = -1i 1= -Lana. a 12.

3aMiHa: sin, .r =

tgx =::i x = arctg:- +

"3!5"6 j=:: sinx=

Bidnosidh:

srnx, tl ,. r-1-"! +nk.k.Z.a6o x=l tl -L-nn.ncz. -:li, 2-.aoo

nicns o6'€ana$ss lsox cepifi Bidnoei t:

Balfil:ai Lg

HopeHiB

orpxM*'o -

l-* ^', '

a6o sin x + cos , = 0 : cos r; tg

2 sin

tcos r 2=

cos';=0]|cos2 r;

lg2

x+\gx-

2=0.

0i \ = 1" t2= -2'

O6epseEa 3aMiIIa:

lgx=Ii x= +nn.neLi tgx= 2ix= arcLe2 -rtk' hF Z. Bianoaida: L t nn: -arctq 2. nk, n, h' Z. 4 2\ 7 sin' 5t - 4' 2sin 5.' cos 5: + cos' 5r = 0 | : cos'z, 5r; 7tg'1 5x 8l,g 5r + 1 = 0. SaMisa: tg 5x = t. 1t'z - 8t - I = 0i i+6 8-G t,= tr = -r.:=lt D=(-8)? 4 ? l=36; JD=6i Z.Z= '"-fin.nczi

*=m tfr!.nezt t + nh' k c Zt r=tarctgi+

-1; x=-!+nh.keZ. 4

! + nn: -! + nh. n. h ez. 24 7) &in, cos r + cos? r - (sin'?, + cos' r) = 0; 3sinrcosr-sin2r=0; -sill r(sin r - 3cos r) = 0; sir']c=Oix=rol,neZ: a6osinr-- 3 cosr=0 : cosx; tgr 3=0; tgt=3; t=atctgB+fik,hE Z. Bidnoaidb: ftni arcLg 3 - fih. n.he Z. gt 2cosr + sin x _ 1. Tstnx - cosx 2 OA3: ?sin r cos r * 0 ] : cos r; |tg t - f + O; tgz+f,: x*ar*ef,+nn,nez; 2(2cos r + sin,')= Tsin i. cost; -bsin r + 5cosr=01: (-5cosr);tgr-1=0; tgx=ri.x= n_+tt4n€L.

O6epEeEa BsMirra:

3 + nn, n e Zi = 3i x = arcl,g 4 + |Ek, h e Z. tg x = 4t t = ^rcfg Bilnosi'b: stclg A + TLni arctg 4 + rht n, h a Z' 5) 5cos'zt - 3sin'zt - 2sin.:c cos t - 2(sin'r + cos'zt) = 0i -5sinz.r - 2sin r cos.r + Scos'x = 0l i (-cos'zrrt \te'E + 2te Sauiua: tg x = t.'t'z+21-3- 0i

Ng2

t -

4trg

t + 3 = O.

O6epEesa BaMiEa:

111111ktgSr ;: 5.r = arctg ; 5,he'' nnnllnk n, k ez. . i BiAno1idh: i'n+:b' ;^tctc; - i' 3) cos':, + 2sintcost + sir'zJc+ 1=1 2cos%c;1+ sin 2t 1+cos 2'=0: sin 2-r- cos 2.r=0 1 : cos 2-r: tg 2n - I =0: tg 2t -li 2x _! + nn, n.zt x=-;+;,ncz: 41 3sin'z.t- Tsinxcosr- l4cos'x 2(cos'? r + sinT r) = 0; sin!x - ?sin.r cosr I l2cosz r=0l: cos, xl tg'zx - Tlgx 12=O. SaMisa: tg , = t, t' - 7t + 12 = Di t'= 3t t2= 4. Lg,

452

838. 1) sin'z, - 2 . 2sin t co_s r + 3 cos' x - 0 | i cos2 BaMiE&: tg r = t. t, - 4t + A = Oi t1= 1t t2- 3,

O6epEelta 3aMilta:

tg 5.'r li 5r

r + 1 = 0; tg r

BiOnosiab:

t - t. t' + t -

!!+nn,neZ.

837. 1)sin't+ 0,5

€2.

3 -L4 + ttn: arcte'5 t nk. n. & e l. 6) Ssin'.' + sin.I cos r + 4cos? r - 3(sin, r + cos, r) sin r cos. + cos2 r = 0j cos r(sin r + cos x) = 0; coat-o: x=!+nn.nez:

O6epEeEa sanriEa: sin'z , = 3; IcopeEiB lreMa€;

sinz

ftk, k

tsy=l; y=!qnn.rg7 4 tg t = 3; r = arctg 3 + nk, h € Z. Bidnoiidb: !-fin, arcta3a n*. n,n h- 2. 42) 5sin'? r - Ssin r cos r + 2cos, r - (sint r + cos, r) = 0; 4sin'zr... 5sin, cosr +cos3r=0 | cos, t;41g, t- Stgr+ 1=0. SaMina: tg r= r. 4t'-5t +l=O; D = (-S), 4.4.1=9t

,6 r, ,.'

5*1=r, r 2.4 ', =!--q=!. 2.4 4

O6epEeEa saMiEa;

1gx=ri x= 1t_ +ftn.neLl !.. , = *.1n!*np.1r.7. '4 4 Bidnoeidu: \ +rn: arcteL - rik. n. k.:2. -4 4 5n, - =

r- 3=o'

lll; anrEEPA Mep3rqKA. r. ra iH. AKaAeMiqHri piBet" llllii:ill:l;ili:1

ilililli_tl:j:.tt A'lTEEPA Mep3rrKA. r. ra

iB. AKaAeMi,{Hri piBeHb

l:it 453

3)6sin2r 2 2sinrcost l4cos?r. 3(sinz 'r 'cosr.rl=0: 0l:co'.r:3tg x-4tex -1=0. Bsin,.r+4sin SaMiHa: tg r. l. 31': ' 4/ . I 0i -4-2 4-2 I D 4, - 4 . 3 . 1 = 4t ,l-D = 2: t,=-2.3 =-Ji rr= zB= r.

2cosz t + zsin r cos ir 2(sin' 2sin n(sin x - cos .T) = 0;

sinr=0: r=rz, ne Z, r =! +nk- h eZ.

a6o siLt

+ cos':

t) = 0i 2sin'?t+

lc cost=0

: cos]';

2sin T cos.I=0;

nn !

eZ.

2."6 sin:r: cos

slan ig!1 l; o.[3: rsin x 4cos.r' 0 5 sin.r - 4cosx 3 2

x+acctel-nn,ncZ: 3(2$n r cos x) ssin t- 4cos x: 6sin x 0:tsx sinr .os r. o:cosxilg.t,l

r-r.,

Scos

cos'i srs.r 4 /0: tg +;;

ssin

4'os x

-It nn,n -Z'

- cos't) + cos, + 1= 0; cose, + cos jr + 2 =0; cosz Sa]IiEa: cos t = t. t2 t - 2 = O: t.= 2" t,= -1. O6epseta 3aMiHa: cos t = 2; (opesiB HeMae; cos x = 1; x=-It+fin,nEZ' flpu n = O: z = r - Hafi6i"tbrrt{i BiA'eMsnft lropiH6. 0,5

t(sin t -

2sin n cos,

cos

t -

cbs

t + 2 =0'

(sin'z.'

+ cos'zr) = 0; sin.!cos n-

cost

= 0;

cos x = 0 I : cos

uan6i,rsmrs

Brdnoaidt:

454

Bi,q

x=i,

Bidnociab:

x=-|., opx*=r r.= -X.^=+

:::;-ff;,

-L. sin 2x

,in' 2,

.nlt

! +942

zsinzx=":"J,";";*,

sin2.r=-1: 2x= !tnn,neZ:, 242 a6osin2x l: 2x n ,nh.keZ: t Bidnoaida:

-1; x=-!+nh,keZ.

a4s. r) 2sin2.r =

net4k=o

n rnn,n-z: n

rnk.k.2.

n e7..

a"in'.lo"i.in , r o. sinr=r.3t, 2t 3=OtDt=( 1)? 3.( 3)=10; ,,;'i; .lE ="To. r.=l '/ru. r^=r vro.

BaMisa:

t; tgt-1=0;tgt=1;

x=\+nk'keZ'

O6epEeHa aaMiHal

'= t, "=\ n=-?!. 2

npvn-o

r; tg x + 1 = 0; tg r

'"t- o, oflt, cos,r*0i,rF -an,ncz: 3..s'? x + 2sin r 0; 3(l sin:.r) 2sin -r 0; 3sin'z-r l2sinx r3

+ cos r = O : cos

2) 3 cos,r .

cosr=O: r=I+nn,neZ' a6o sin

KopFHiB HeMac.

242

BiAnMiA': -n. cos

jr 3 0r *"' - t:

2,in2,

839. (1

84O. sin'zir +

a6o 2cos

cosx=o) x=L+nn,neZ;

1= 0i tgt=1;

tg,

t + 5 cos'z t 2(sin'z r + cos'? t) = 0; 0l:cos'r: !e r 2'6rer'3=o: 3eos'x sin'x-2J3sinx.os-r, 0: rer \6=0r ugx=J3r x--f, tnn n't' {re'-Jr]'

5) 3sin'.r

x=f,+!,nez:

a6o sin iu

+ nh, n. h

o; 2:r=Z+nn,nez;

842. cos t(sin jr + cos ,) = 0;

Bianolilb:

2r(2cos.r + 3) = 0;

Bilnoai}t: !. ,4

1JI -arctg;r \ni -;- rk'n.k -7.

Scos 2,. = 0; -cos

npun=o:,=x.

r= \+nk.hez.

Bidnosidb:

+2(1 cos:2.r)=5;3 8cos2r+2 2cos'u 5=o;

cos

rl -Fi .{=-arcigg+\n,neL:

tsr= '4

-2cos'x

O6epEeEa saMiEa:

tg.x =

c9s2{

a41,61

nopeErB HeMac:

1 ,R gnr= r-.,/io e l ir={-r) ar$rn ! _n,,,.2. Btd,oetabi (-r)" arcsi nt f; *no,n.z.

cM$Hii KopiH6.

-L. 2

li:i: AITEEPA Mep3rqKa. r. ra iH. aKaAeMiqflr,ti piBet"

1+ J1o

iliillli:i;i;iiiil:

::li:al:il:ilil:l AITEEPA Mep3rrK A. r. ra

iH. AKaaeMiqHrn piBeHb

:ii::; 455

er g. l -

cos2x

-4r1

cos'2.r)

I-

4cos' 2t + Scos tcoe 2i + 4cost 2t 4cos 2x - 3 = O. SaMiEa: cos 2t = t. 4t' - 4t - 3 = O)

- 4. 4. (-s) = 64; JD = s;

D = (-4r,

rScoszx-5=oi

4cos2

2r +

4cos

2t +

3=0

: (-1);

4+8

4-A 2.4

seMae;

D.t at' 4 4 3 .oszr = 3'i

!;+ nn, n ez. 4) 3 + scos t = -(cos' .t - sin' .'xcos'z t + sin',); 3 + Scos .' = -(2cos': r 2=

1);

1 I 1\ cosx -t; r =-Lln-arccos;J+2rn' r ezi r=!?+zrn,nez. 2n

t-+zftn,neL

D=(-7\,--4.2.s=25: JD -5; t,=1!-s; O6epEeEa 3aMilra: cos , = 3; &opesiB EeMae; s6gy=\; t = +!+ 2nn,n ez. BiAnosiab:

t:I+

2nn, n

= t.

sin2x

.,42 -5 |

-2 Jn

O6epaeua saruina:

cosx =

456

fi 2.znn,nrz, -Dt,l2sjr = larccos-iH.

xopeHrs

l: ncva€i co32.r '

$sd

2t=L!+2nn.nL7.:

ll:liI

ffi

+ nn. n e7..

12t

2x 1 lfrarcsin I I nn,ne\i

= t-l\"| ! +

nn, n c Z:

!: a\!. r 62. 122

aKaaeMiqHrlr piBexu

$+ !, n e z. ar sin.x=lcos,r-st".if".",-, "i",r), "i".,=.*,. r, \22J\22) (1 - cos'zr) cos r=0; cos?r- cosr + 1=0i cos'!r + cos r EaMina: cos r = l. t' + t - I = O', D = l'z - 4 1 . (-1) = 5; 1 6, r --r+n6-E=s, ,.= '2'2

fflJliii:iirif$

1= 0.

O6epEeFa 3aMirra:

(.r Js<-r.]: -l cosir -r-.,6 2 i ropeHrs seMac | 2 cosx . Vbj-I. r = larccos\J - 2nn, n cz.

BiDnoai\u:

- ;-;

ii{: arrEEPA Mep3rex A. r. ra

8-4 I +; t,- l!=3;: ' 2.4 2 2.4 2 t,=

Bionoaiat Gr)"'

D\=2, s. (-b, = 2s; Jo = Jm; O=-'*u@ ,

a = 1-11"t

eZ.

\t'z + 4t

Bk)nosiAb:

srn,f,

3 = 0;

sin 2, = -3; (opeHiB seMae;

t + 3 = 0'

lPa-ssin'=0; o,43: sin'+oir+nn, ne Z4cosx-ssin'/n-0. n:gSlj!L-g:14 o: 5cos,.r - 4.osx s=0. cin

0; 4cos,2l + Scos 2r -

O6epEena BaMiHa: Tcos

844. 1)

SaMisa: cos

,to

s) 7+2sin2.r-r,5rgl--':""1 - o; oaa: t, \cos.r srn -rl ?+2sr2r+l'5{sin'zr' cos'r) 2 =ot z v 2sin2r r 3- =0, cos.r sin.r 2 sin2x zsin'z2x+7s\n2x+3 =0t 2sin:2r' + Tsin 2t -3=0' "i SaMiHai sin 2, = t. 2t' + 7t + 3 = 0i D ='I' - 4. 2. 3 = 25: g, 1"__!:J=_!. Jo 5,,.' _7_5 ' 2.2 2.2 2

O6epnesa BaMiEa: 4! RopeEiB seMa€; cos r

I - cos.r i 5) 2cos'.r-1 gcosx+6=4 -.gcos t + 6 - 2 + 2cos t = Ot 2coB2 x 2cos2 t - ! SaMina: cos :r= t. 2tt 7t+3-O:

r6i

n!,n ez; 2

-5t3 D=b,-4.2.2=9..ID-3t \= -5.3 ;.2 -4: I, z-2 =-t.

Bidnoqidb:

+ 2nn- n e7..

t=!!+nn,neZ.

2cos"+5coB.r+2-0.

= t. 2t' + 5t +

)

-',].

O6epHeHa saMiEa:

Bianosiab:

cos,

2) 4(t'2- cos'2x) -7 co.2' -2.r-':"2' 4 - 4coE'2x + 7cos 2x - 1+ cos 2.rc 4cos' 2r Scos 2r + 3 = 0. 3anIiIIa: cos 2, = t. 4t' 8t + 3 = 0i

'i,"^.".2.

gaMisa:

"o"'='S

(o l;6 'r"". l.

( 2ft r r) 2r-+f tr - arccos;J |21tn,n'Zi 2x'Ia-znn.ncLi "o.Z'=-i,

ixopeEiBHeMa€

aidnoaiab: xarccos@

O6epseEa 3arriEa:

9: Kopenin "n"2r = 2'

loo

ilillliii:ltlll

arccoe@|

+ 2nn,

tu e

AnTEEPA Mep3rrx A. r. ra

ir.

AKa.qeMi{Hratr piBeHb

lil:

457

b\ 2 (2cos' 21 1)-2.1119q?1-scos2x-0' 4cos'2x 2-l cos 2t - Scos 2x = O; 4cost 2t 4cos 2x 3=O' BaMiIla: cos 2, = r. 4t, - 4t 3=OtD=(-4), 4.4. ( 3)=64; Jr=S;

];

SaMiHa: LC;

,,on""ru

*"-.";

ugl=4; '2

!:+

nn,

t eZ.

845. CtoprcraeMoce roroxisocrsMlr:

"in"

z"n1.o"!r; co"' = "oJ

ssin'

osinlcos

; - s cos" ; - 11cos'z { = 0 t cos' +

sin"

ssi^"

};

;

= 0;

tc"

awf, - n

t*;= T,r=-""(--'Jl ,^n.n-zi x=

"2I

2arcle4 | 2\n, n .Z;

z"in"

uln

=,f5.

u/3, {=Iann,ntz:

2 3

t = ""Et |

x=zn,2nn,nezi

= arcte 2rE + nk. k

x = 2 arcte 2Jz + 2nk, k e z.

3"- 2an; 2ar.cte2\E | 2\h, n, h t Z. 447-l)l 2sit]''r+ sin r= (1 sin,r)=0; I - 2sin, r + sin r 1+ sin?r=0; sin':, + sin r=0; sin r(sin r - 1)=0; sin.r=0:x=nn.nc Z: a6osin x I 0isin ,-1, *=!-2np,k.2. Ilpr.rn=0:r=0; npun=1x=n; npBn=-1 .r=-7r:npx k=O x=*: e= 1: r 3r x= ixo*: npxk=t *=l-zn.5] 2-2fi - 2 se BxoArl,rr, ] Dpov 2 2 "-. "*ou,'"

sin

'l tJ

^ u:

a'=oX: te"}+ztc} 3ar'dua: tgI=6. t'+2t-4=o;Dt=1' l'(-41=5; t' =-1-G; 4=-1+J5

= ol.z"os"

y rpoMidioK. Bidno6idb: 4 KopFHi.

2(1 cos'a) + Tcos.r + 2 = Ot2-2coE':t+Icosr+2=Oi r + Tcos r + 4 = O I : ( r). SaMiHa: cos .r = i. 2t" 7t 4 OiD ( 7), 4 2 e1f,=81;,lD 1 , 7+9 ,. , 7 I ' 2.2 2.2 2

448.

O6epEe:ra 3alttilla:

-zcos:

tei--t Js, i= *.tc(t w = t +,li; !, = *.tg( t t | 458

ftn.n.li

Bionoeidd: "l'

4,n;."";- 8""{ ;+ bsi.';- 3co{;-ss,\";=

Bionoliab: 2arc].1g(-l

O6epIIeEa 3aMiIIa:

zar"tslt tnn.n-7:

| tnh.k.z.. ,=!,zn*,*,2LgI -2 r. {= 2 2 4 Bionoaidt: -2arc4! nn., cz; |-zn*.n.t,z .r t .x ,ir' tl."."', sin;J 2t 2zsin;aos;s[.os't

{=u."t*o-

rg{=i. i'-e,fit+o=0, D (3J3)' a.6 27 2a=31 2 t; -t; ^t; t; o/o ovo ovo-vd vo r l;-. '2-2

O6epEeEa saMisa:

j+asi"]*"{

samina:

= o.

tg! = t. 5t' + 6t 11=OtD=6'z-4 5'(-11)=256; t6 ll , i, -6t16 -, 16: i. -6 2.5 2.5 5

-scoJ

4i t,

2sinlcos{-sl-"'.'-"r"'*l \ 2 "r"'')2' o, 2 2 I 2 2' z["."'' . ,x _ ,t - lsrn- tl: t)\/J srn cos 5.os--I5srn---/cos' 222222 -2":. r+0,,6"i"i"*i-t2""*i ot,( z*' l); te'|.a,E"sf,+a-o.

3,amisa:

. J,

4 Oi tt

2r sJa

"in'I

" l- rl trazsinlmsi-slcos';-stn'?;, 2 "t,,'t'lz.) = o: \".*'r-,

6"i";cos; - s"oJ ;

- t. t2 3t

rn{= x.-n 2 +2nh.keZ. '2 .1, I=-I1nh-k,-Z: 2 4 n Bidno'idh: 2arere4 -2 r 2nnt t2nh,n,hcl.

r=+L+nn.neZBilno'iab:

{J =o, 2)

O6epEeHa BaMiHa:

-("-;) ,2,.n.n-Li 2,= t2[ +znn'n-2.

l, *

"."r--

{,"; 2sinxcosr,sl-"'* .i"''), 2l sl-. \ 2

15 5sin'3 + 3 cos'{ + 3sin'{ = 0: 222222 "o"'{ 2sin'x , Gsrnrcosr rscos'r 0l:f 2"."'Il, tn'{-:rL'x-a '2 2 2 2 2 2l '2 !

06epEeHa saMisa:

"o"zr

6"i"1"o"{

4 8 1 3 t,= 4+8 z.a=ir t,= 2.4=-t' =

846.

n[E) +

nE)+nn'nez;

x = 2arctg(

Ji\ + nk, n e z; z

znn,

t-'fi)+2nn,nez;

= 2 arcts(-1 +

Ji)

+ nh, h e

, ez.

iriaAIIEEPA Mep3rrx a. r. ra

iH. AKaaeMieHrar

pieenu

llill{f:i:ilf:ii

O6epEeEa 3aMiHa: cos = 4; rcopeHiB EeMae;

:iiiiiiitiii:i*

AITEEPA Mep3rrKA. r. ra iH. AKaaeMi{Hhr piBeHb

l:::t' 459

12n

x =-:-e6o r Ilpr a 0-2T-2^2n

,-?

,=-!+2,=!

nvttn=t

1) cos" 3aMirra: cos

,e"

Bxoal'rrb

y npoMixcoft);

r=f *z*=$

t"".xoa,'rr,

y rpoMixox);

2ft 4n Bi.Ano6iAb: 2n.

- sin't)=sin x; -2 sin'jr sin;r + 2 =01: ( 1);2sii'zt

gaMina: sin

vr'vrii

a<2-

BiAnoqiAb:-1sa<2.

2) Eijn'r- 2aEiI r+ 2a2 4a + 4- O. gal'riEa: sin r = ,. t' 2at + 2a' 4a + 4 = 0t

849.2(1

cos r + a - .r2 =.O. r - t. t' t + a(1 a\ = 0, [t.+t-=1. tt ai tz I a. 3a reoppMoro Bi.ra I li, .i. = o0 _ a): PiBssHHs MarnMe KopeHi, sKqo -1 < a < 1 a6o -1<l - a<1; -2 <-a<0;

452.

+2nn-nEZ.

, = ,. 2t' + t - 2 = Oi D = 1 4'2 (-2)= u[7 t . rr=-4t -,hz-: t,= I'Jlz Z.Z 4

+ sin

17i

D,=( a)' (2a, 4a+4)= a'+4a 4= (a' 4o+4)= (a 2),, PiBIIsErifi Ma€ &opin6, snqo ,r > 0, :(a-2r'>-0IJp]'a=2. S\{\o a = 2, t' - 4t + 4 = Ot (t - 2r' = 0; t = 2, npore sin r = f, roAi sin, IIsnIIs nopeHiB

= 2. PiB'

Ee Ma€.

BiAno'iAb: aalrorc BE '{eIIEs a IIe icHy€.

O6epFeHa saMiHa:

r Jrzi xopeHr! Eex,ra€ (-ttJtt

sinr.=

"r,',='r;-t, urlr rrpr

= arcsin

1 lr = -

arcsi

^ aso.

= Gr)"

ss3.r) rVZ

a-.-t.],

2) Jz

*"sin@l +M,nezi

li;., gil

n[',

t * n.

854.

2) x,(x

BiAnoqiAb:

= o l,

"o"|;

"i"'i

3\ ta(E + 2\ + 8(r + 2) - 0; (r + 2)(r' + 8) = 0; xt2 0',x 2a6o.r{ t8 0l xopeniB Hevac. BidnoBidh: -2. 4\ (it3 - 1\ - (2x'z - 2t) = 0; (r - lX/ + r + 1) - 2r(r -

tef,

-t

= o;

|=f,r "*, *.2; x=L+2rh,kez.

Ili' +r.=r, '

1, t'=a(r-a):

l,=

- 3i t"

PiBEsgns MarrM€ Kopelri, triDro -1 < 2a - 3 < 1 a6o -1 < a < 1| BiAnosiAb: 1 < a < 2. 2) cos" + 2 cos r + o'z - 6a+ 10 =0 SaMiEa: cos r = ,. t2 + 2a + az 60 + 10 = 0; D,= l a" + 6a - 10 - -la' - 6a + 9\ = -la - 3)'' PiBHfisBs Ma€ Hopilrr', axqo ,r > 0.

-(a-3)z>0trpra=3. fipna=3t'+ 2t + l=0;(t + 1)'9=

2 < 2a <

1 <a

< 2.

1, pinng:rHs Ma€ xopiHl'.

BiAnosiAb: a = 3.

ufespl

Kirrbrlicrb

6Dvxr II 6Dvxr

CwiItr

Mep3nrk A. r. ra iH. AKaaeMiqHul pisexu :i:li:ii'i:ili:i'.;i::

140

1) = 0;

H"Mac.

1) sin'z .is (34 - 3) sin , + a(24 - 3) = 0 SaMiEa: sin r = t. t' - (3a - Aft + 4(2a - A') = O.

i:::i:

(r-lxr'?+r+1-2,')=Oi .r - I =0:.r = 1 a6o.r' - x + 1 = 0i KopeHis BiAnosiAb: L 855.

851.

460

5, + e(x

BiAnosidb:5-

-0,

Bj€ra 3a reopeMoo '

-2i q

- 5) = 0; (' - 5)(,, + e) = 0; ,r 5-0; ,r- 5a6o.r'z I I - 0; KopeHiB HeMa..

,47-r

-cosf,

r)6r(1 2\(x ' 2\ o: r 2=0; xz=2 a6o x + 2=O; rx=-2,

= 0 a6o BiA MiAb:

rl rl x -2"i""!+zs'"t."'i=o; zsrn2\lsrn-2 - cos 2) =0; nn, n ezi r-2nn,nez, "i"|= o; |=

t'{tz; '{n,,{Ez, *o*v iF ''V77; 'F i ,Vra, ,V42.'V33, 'o..v Jz. t,fra:

,V33r

st fr# i i6rr 9225,a!t2s, Vts 'vs, 'ouy al {F i {6; '{tr ''iF, ,o*v iEr ' i6.

z"i"l*"i**"'r "i''i--"'i

aoo sin

Itinbriicrf, Eilieflo

5 40

0,05x

42i

0,4u

Hexafi .f, r 6pyxry I BrAy, y r 6pyxry II BnAy. BMicr Hircenro B rrx 0,4v r Bi,qtroBi,qEo. vcboro 6p]'xry aBox Br{aig trorpi6so Bs.Err (, + y) r, a6o 140 r. I piBnEEHs cncreMn: r + u = 140. ycLoro Hi&enb B 6pyxri ABox ErIAiB (0,05r + 0,4y) r, a6o 41 r. II piBEflEEn cscreMr.r: 0,O5t + 0,4v = 42, ]r-o.al J-0. ax - o. ae = -ro. )o.Os' . o.ay lo.ob-r I 0,4y 42t 0,35' = -14: t: = 10i r + u = l{Oi a = 1OO-

r r i

- 0,05r r ra

l,+y=1as. +zr

BiAnoaiAb: 40 a

illiftllttiilL

100

AIrEEPA Mep3re(A. r. ra

iH.

AKaaeMi'{Hrfi pigexu

iii:j l6t

6. Po3a'g3yBaHHq rplroHoMerptqHtx piaHtHb MeroAoM po3KnaaaHHt HA MHOXH}IK}I

856,

2, cos ,. = 0; 0; 2, = 2x=!+nn,neZ:

1) 2cos

cos

a6o cos

,=\+T, r.z;

a) .E cosr(cte,. -

, - o; x=!+2nk,heZ.

Btdnoeioa:

sin 2r = 0; ht=nn,

a6ocos3"r=o:

ne Z; r =Y,

3x l+

nk.

Y: L +4. n. * ez. 263 3) sin ,(2cos 2t - 1, + (zcos 2, 1) = 0; (2cos 2t - lxsin ,r + 1) = 0; 2rosr I 0i cos2x=!r 2x t\+2nn.n.Z: ,='[ "".".2, sin,r t,x= 1 2n*.kcz. a6osinr.,l =0:

z sin

x[+ nn: :+

znk, n,

k.z.

r (tg r + ,6) - (te, n J3) = o;

ig'+16=o;

tgx. =

-!+ nn;

857. I ) 2sin 4r sin 4r = 0; a6o.ros

(tg"+.,6)(2"i""-r)=o;

nh, n, h

62.

cos 3,r = 0;

4r=nr, neZ; x=!,

n eZ;

*!,*.2

ax 0i 3x=!tnh.kt7: "=i

br = 0; 5'

Bidnoeidt:

= nk, k

!: 4. 45

n. k

=Y,

e Z;

(te' z

2r(te

Ji ,

nn, n

sin.:c=1;

ez.

"o"r=$,

"mro,

'6sinr=1; "*,=;t

"t",=f,

-2.

*-l'-.,,1

"i"[]

x=!X+2nn,nez;

z") =o; z"in

,, *(" . n"l

cos---=o:

n nn.ncLi x n 2nn 418 -,ncLi !=L-! -np.1112 2 2 4

- Iz 2

t"""

tor+11 \2 2

2al

)

=0;

. (^ n)=u: ^ ox^ rr nn-n. Li - ^ nn,n-L: x=-+-,n.(/i - rrx 4 4) aoo cosf+r ,n) o, a,tno=\,nu.o.t, a*=|-! anp-a.71 s'nf o.r-4.J

4.r " tnk.kcTi x " t"".k=2. 4 16 4 nnnnnk :-: Bi.Jno6idb: -n.k.Z. 246164 -+-r

t + tl = ol

+ 1) = o;

x = ardg\E + nn, n ez)

ii!: AnTEEPA Mep3neKA. r. ra

f}'arcsin

+ 2nk, n, h

t: z @cosr=I;

2) 2sinrcosl=1; z

ir {

,"'"(.,-;) "."(,,.' ;) =.,

ez.

rgr-\E=o; tgt=J5;

nn:

10,

neZ;

, =!

is''(is' + 1) 2(te'+1)=0;

(te' -.8)(te"..,D)rtsir

462

-3n . 2o*, a. 1.

a5a. 1) 2coslcosr=

si:n4;,=O)4x=nn,neZ:

"o"=-f, '=t(^.X)*",u,o.t,

\2 4) 4) . /9-" r) - 9x n 9r srnl2-AJ =u; ---=nn,n.L: - 2 *,nl a6o cosl 2 4 2 \2 4) o,'.I=!.nk.h.Z: ! = \ + n*. * ez: :c = ! + 2nh. k eZ. 242 -n2nnn' ttronostob: +zltl?,n,heL, 1g+ Ii

^finfifik Blonoanb: -i 2) -2sin 4t sin 5.t = 0;

a6o sin

sinl; r'l o;zsin 3 l * ll = o. z"r.f 9" - ll "..1\.2

-',8; x=-\+nn,nez;

(-:ohI+

(ctsx - 3) = o; lctgr-:1(.ifcosr+r)=o; 3j r=arcctg 3 +nn, ne Zi

3lsinb-r

a6o2sinx r=o: "lnr lr x=t :':'in' nk,kLz. Bidnoeiat:

a6o .Ecos:r + 1=

Bianosidb: arcts 3 +

h-z:' -I-# r',

Bianoaida:

Bilnoaisa:

eZ;

3) +

3=Oictg

cNg

I r "i, i-n*.,.a-2.

2) 2sin 2.r.os

A60 te;t+,tE =o; ts,=-Jt; r=-arctglE+nk,keZ; s6otgt+1=0; tg t = -1; , = -!+ n*, eZ. ^ BiAnosiAb: l:^rclg\E + nn; !+nm,n,meZ,

iH. AKaAeMi.rHr4i

piBet"

iililililiii:iii

ljillii:.i{ilf;:;; mreSPA Mep3reK A. r. ra

iH. AkaAeMi.rHr4i piBeHb

iii:

463

459.

rrzs,"fcos(,

x f;= znn, oez;

ff)-', , ]*"('-iJ='' -"('-#)=''

61 2sin2xcos2x+21+cos2x-l .os 2-r(2sin

t=!:+2nn,nez:

1-s*l rsini.r 0: z"i.,lr-'l"o"ln r'll "r^l\2 ) \4 .r \4 x n.nn.ncz: *=ltnn.n-z:

:r'

aio,o.ia,,

1- o, -",

t(" - ;)

lt!; x! + znn, n, * ez.

"=xft*!,n.2.

2sil:. 2x

a6o 1

sin

= O;

sin,

1; a

T, n EZ. 5) 2sin 2r sin(-r) + sin t si'rx=Oit=nn,neZi

a 2nP,

*. z;

x2]

+ 2nk. k e

sin

.jr)

2, +

+I!,

cos

"o"*

â&#x201A;Ź2,

9, *=tu'""osB + nh. k eZ. 44

1*""o"1 , fih.n.heL. 4

+ sin 3r) + (sin 2r + sin 4r) = 0; zsir.

-r _o: -r

sin 3r) =

1) = 0;

x=ttl'fi+!,nez.

cos

x + 2sir 3r cos r = 0;

= o:

' n +nn.nezl 5{

1I o, "0. "ln 2 = 2 a6o cos;=o;

op.

a. r, , -2nh < 'R'Li

f,=!+n*,^ez; r.=n+2nm,n. z. Bidnoaida: \ t nn: 4; n + 2rtln, n, h, m e z. 25 9) (cos 7r - cos 3r) + (sin 8r + sin 2r) = 0; 2sin 2r sin 5re + 2sin 5r cos 3n = 0; 2sin 5r(cos 3r sin 2r) = 0; n-a*l-","2;l -o: 2sinsx 2sinl n 5*l"o"l n 'J=o, z"i"s'l"i"l 12 t4 2t \4 2l \ sin 5t = O) 5x=nn, ne Z: x =!!, n eZ;

"i"l!r-rl \2 4)=0,

sin 2r

si\

n, ne z.

iial AITEEPA Mep3nrx a. r. ra iH. aKaaeMi.rHr4t piBenb

0: zcosr.zsinfco"{

E!-!=n*.xcz, !!=!-np.1,.y, 2 4

10) Jfsin2.r-2sin?'sin(-2r)-O; Jf

2r=( \r.]+nh,hez; "i"2, = -f,t

464

x=L

105 xnn-x3n -lxnlaoo cosft-aJ=u; 2-a= i+tin, ncL, t= -+n^. ^.zt 3n x=-+nmtnez, n 2nh 3n -;' - nm, n. h, n -2. Bidno6'db: ;'i;o---'t

a6ozsin2t+1=0;

++5,

ez:

fl2fik-+ .keLi

P.7.

= 0; sin r(2sin

2cos x(sin 2.ir

= 0i

BianosiAb:

Biotuoliab: nnt (-1rr

Bidnosidb: nni

8) (sin

.6.

- zsin r sir 2, = 0; 2sin 2r(1 si.' 2x = oi zt = nn, ne z; r=!, nezl

* r^0.

+ nn, n

2x = l-|t'-t

a6o4cos.r-3=0:

1) 2sin, cos r + 2sin r - (cos t + 1) = 0; 2sin r(cos t + 1) - (cos, + 1) = 0; (2sinx-lxcost+1)=0; 2sinx-1=o; "i""=]' '=CU"fi+ +nn, â&#x201A;ŹziZ+ 2rtk, h e a6o cos r 1 = 0j cos t = ti r = fi Bianosiab: el\"X+ nnt it+2nh,hez. 2\ 2cos' 4x - cos 4t = 0; cos 4t(2cos 4t - 1) = 0; , cos 4x = 0i 4t=L+nn,neZ; r=!a!!,neZ; j, 4x=t:+2nk,hez; a6o 2cos4' r=o' "o"ar=

- 3) = 0: sittr=Oix=nn,neZl

860.

a6o 2cos

I I cos2x- 1=oi

sin': .r(4cos .r

ff'I!,,,*.2.

Bidnoaida: \"+Y: tL tI!,n.eez. 3) 2cos r cos r + cos 2t = O' c$ 2t(2.os x + l, = Ol cos 2.r =o; 2t = \ + nn, n ez;, = +\, n ez; f,

2sin 2-r cos 2x

! - nk. k c z. x=t-lt''t n tnh.k.2. 6 12 2' Bidnoeido: ! r $r 1 ry' ' ! r!, o, u. z. 42 122 7) -2sin 2t Ein(-r) = Ssine t; sin t cos .t sin .t - 3sin'2.f, = 0; sin2x=-1: 2

"-(l l=0,"''('-l) .u" *"(; ,,) =0, *"(*-l) ='' rz !-!+nk,hez; 4x =4 + nk, k e z:, =#-*, u.t. ! + nn:

-0i

a6o2sin2x+1=0;

=0,

aidnoaida:

2r I l)

cos 2* = o; 2r = !

.0,

tllli:tlJJlii$

('6

2t;

+ 2 sin 7:c) = o;

Ot 2x = nn, n

:i!f!i.:iilli:i:il:.::

sin2,r+ 2sin7rsin2.r = 0;

e Z;

x=Y,n

eZ:

uresPA Mep3rrKA, r. ra iH. AKaAeMieHrli piBeHb f.i:J 465

a6o 2sin?i+ J3 =0t sin?x= -;;

x=( 1t*\L+!!.hâ&#x201A;Ź2. 21 7 Bidnoaida: "": r It' " 221

7x =

(-lt'i !

7) (sin + nh, k

eZ',

"".n.kcZ. 7

r cos, + 2sin r= 0; 2sin r(cos a + 1) = 0; sint=O;x=nn,n.Zi a6ocosr+ 1 =0; cosr= li t = n+ 2nk, k e z.

861- 1) 2sin

BiAnoqiAb:nn,neZ.

2sinrcos, cos,-(2sinr- 1)=0; cos r(2sin.r - 1)-(2sin:, 1)=0; r 1)(co3r 1)=0; 1; r=1-l;"\+nn,ncz; 2sinx I o; ";,'r- 26 a6o cos x - 1 = 0; cos r = l; r = znk, h e Z. Bidnosidb: l-1l L + nn. 2nk. n. k . Z. 2)

(2sin

2sin':4r sin 4jr = 0; sin 4r(2sin, sin4r o; 4r nn,n z;x f,!,n.t;

466

8jr

= o;

sin 2js); 2sin 3:r cos 2r + 2sin 3r cos 5r = 0; 2 ein3z.

cos! cos!

= o;

s) .E cos5.r

+ 2sin(-2)cos5.r =

cossa(.rE 2srr

2x) = o:

2105 t. J2 2sin2r.. o; ,,"r-=+. 2x=t)f X+nk,k.z: x t t: nh Bidnoqidb: | ; (. ,.,n ir; ;-n-h,7.

ftk.h.z.

l) sin,r.sin,3t t, l-'osxrl 'os3}-1. 2222 1 cos ]' + 1 cos 3ir= 2;2 - (cost + cos 3r.) = 2i 2cos 2xcosr=0; * n,,, cZ, x=n +rn , n. L, coe2r = O, lz* =!242 cos

= 0i

BiAntuiAb:

x=" -ak.hcl:

!+Y.oez. 422

" n*.*-2.

L+nk.kez.

1+-"2'

2r cosj.r -.osz 2.r + cos'a. t.5, "osF , "i"6'= r.l, + (cos 1 cos 2x + 1 + cos 4r + 1 + cos 6r = 3; 2ir + cos 6r) + cos 4r = 0; 2 cos 4,r cos

l. l4x=

cos

0i cos 4,r(zcos 2r.

1) =

n Ix n nn Bt 4.nez, ?tnn,ncz.

l"o.z' Bidnoeida:

I'":

r n' u=Lln-!l-rnu.u,t,

ft ft!.a-7, 1L-nP,Ps7. 843

0; [:'"41= 2cos2x+1=0i

I nn lr ^s.-,n<L. I

l, -i,*.a.2.

3) cos 2r

- cos 8r + cos 6r = 1; 2sin 5r sin 3r - (1 - cos 6r) = 0; 2sin 5r sin 3r - 2sin'z 3r = 0; 2sin 3r.(sin 5, - sin 3r) = 0; 2sin 3a. 2sin.r cos 4iu = 0; 4sin 3, sin r cos 4r = 0!

sin:.r=0, n,,,nFz. l' "{.^'z' [3.r sinx 0. x=nk,ktZ, x-fik.k.L. cos 4r = 0: cosar=u: n t nm.n.z:

Bidnosidb:

2, + cos 5 rl

862.

2sin,y I 0: sin,r .1: r=t-1f !+nk.hcZ. 26 Bianoair Y. t-ltt \ + lth. n. h â&#x201A;Ź 7.. 46 4) 2sin 3jr cos r + cos r = O; cos jr(2sin 3r + 1) = 0; cosx O:,r fr tnn.ncz: 2 a6o 2sin 3x I 0i sin3r -': 3r -r-ll'r'' -nh-n-kc7- i=t-lr' t:-+':!.k-726183 Bidnoeido: !-nn t l)^'l 2183 5) sin x + sin 3r + sir 2r = 0;"'1.a.F=Z 2sin 2r cos, + sir 2r = 0; sin2r(2cosr+1)=0; sin 2x = 0,2x = nn, n. Z; x=!,n -Z: 2 l. t a6o2cos,r r 1 0: cosx ,2nh.hcL. 23 -2n R'an^Aiah !!!. +!!+2nh n he7 6) 2sin 8-r sin.r 2sin2.rsinx 0: 2sin.r(sin 8r - sin 2"r)=0: 2sin , . 2sin 5r. cos 3a = 0; sinr=Oir=nn,neZ; n! a6o sin 5x 0; 5x nh, k eZ, t , o, ,, a6o

a6ocos3x 0: 3x

+ sin 5r) + (sin

3.r 0:3,r,rn-nIZ: I=!,ncz; ll 7x n I nh.h.z: ,=!+?!!.k,2 a6o cosTr o: 22277 -.3l^3xn-n2\m aoo cos 2 ui 2 2 "^,.-Lt x.- 3t 3 .ntL. -finfiznkn2nm :i :Bidno6ia)b: : + .n,k,mF7. s

2sin 3x(cos

-nm.ncz: t"n-nt.^.2. 263 fini !' t !' , !" . n. P. rn.2. 563

fax

!i::i A'TEEPA Mep3riK A. r. ra iH. AKaAeMi.{Hrr piee}ts

:::iitiiiitiii!: 'tiil:iiiii:lii:i:i

l"=E-T.^,r

AITEEPA Mep3neK A. r. ra iH. AKaaeMi,{Hxn piBeHb

*:l

467

sin'2ju sin'z3r sin'z4r = 0; r - sin'z 3jr) + (sin'z 2r - sin' 4r) = 0; (sin, - sin 3r)(sin r + sin 3r) + (sin 2r - sin 4r)(sin 2, + sin 4r) = 0; -zsi'l r cos 2x . 2sin 2x cos x - 2sin r cos 3r . 2sin 3r cos r = 0; 2sin r cos x . zgin 2, cos 2r + 2sin r cos r . 2 sin 3r cos 3, = 0; 7) sin'a +

lnloe;rr-.atxu

9=nh: n=3h.ro

BianosiAb:

(sin'?

lI= +-,meL. 184 +-.meL, a4

+,Iezi

sin 2r sin 4r + sin 2r sin 6r = 0; sin 2r(sin 4r + sin 6r) = 0; sin 2iu . 2sin 5, cos r - 0;

1- cosr.=ts,r siD.x: oA3: ,.; "",^czi r-cos.t lll';-"'"', sin.rll-cosr) cosx(l -cosr, sin.r(1-cosx) ^.

(1- cosxxcos.r -

sjn

fr-*"-=0, cosr - sin.r I

cos

= 0,

+f,+

nn, n

ez;

cos'?

l'x=nk.hez.

lx=!+nl,leZ: t=!+nI,IeZ. LZ t. keZ: L+nl.LeZ.

+ cost 2r + cos' 3$ + cos' 4x = 2;

2r . 1 + cos 4ru 1+cos6, 1+cos8r

1 + cos

222

2t + cos 8t) + (cos 4* + cos 6r) = 4; 2cos 5r cos 3r + 2cos 5r cos r = 0; 2cos 5r(cos 3x + cos r) = 0; 2co3 5r. 2co8 2r

-+-+-+-

\+nm,me7. 4

lx= 2LfiR.neL.

s9t

nn, n ez.

2r = \E(cos, - sin r); (cos' * - sin' r) -'E(co"t (cosr - sinrxcosr + sinr) - 1E(cos.r - sint) = O;

cos

lcos-r '

- sin.rllcosx ' sinx-J2l

cosr sinr=0rctg.t-I cosr+sinx-rE=0r

cos

cosx-sinr=0, lcosr'sinx-Vz -

x + sin

sin

z, 1

-znp.*ezt

x=!+nn,nez, z=L+2nh,kez; BfinosiAb:

468

, =I

* 2nk,

nl t-+ +-nh I

2+cos

"."'

iH.

aKaaeMiegnr piaent li{lll:}i.iilil:.i

cos 9x

+ 2cos 3x = 0;

I L6r

iitiili_:ilii-1t1:jii

6rc

nn-lnnn 6:+ 3163

+ 1) = 0;

2x 2fi

+2th h ezt

l, = +!*!! 193

eZ-

. 1Fcosl2r 1-cos10.r r

= 0;

o. rtx=|-nn,ncz. -=h-#.,,t. n nh,he7:

.^finn 22

3r;

12x + cos 10.t = 2; cos 12r + cos 10r = 0; 2cos 11r cos

cos11x = |lcos'rru: = o,

k.z.

Mep3rrKA. r, ra

'22

!+rm.meZ.

:}il: AITEEPA

2';

.lz : ,Er {cos'+{sin'=r; .12

'12 n .... rt srnl.-rn I -t.) .n -l=r, ,-\=I sin4cosx rcos-arnf ,. 4 z

2cosr

o;2r 2cos 6x cos :3': + cos 3r = 0; cos 3js(2cos

= 0;

li x=ft -nn.n.Zt

-O:ctgx

= 0;

Big6ip ropesis:'gas. pzcyso$.

cos,

5r=!+nn.nL7. ^-'-*"" "' l,=" '-10 "' lcoss:=o. l-n,rk0. 2x " Inh,k-7. x" -tr'!).6a7. Icos2r lcosr=o: ' x=!-nt.teZ: lx=!-ttt.tcz. L2L2 -nnk BidnoBidb: to|--,nezt i,;,k -r.

t + sin 3:t = 4cos2 xi 2sin 2r cos r 4cos' * = 0; 2cos x(sin 2x 2cos t) = 0; zcos (2sin t cos r - 2 cos t) = 0; 4cos'z r(sin t - 1) - 0; . cos.r=U, ln lt=-1fin-naL. | 2 5) sin

BiorLoliOb:

4 + (cos

BianoaiAb:2fik. k e Z.

= 0;

Bidnoafit: 8)

n e L.

lstnx-t=o: L

ctg.t-1-0,

lx=2\k.kez. t=L+nm.meZ, 4

tir + lr t+

sinsx = 0,

tc=21th,keZ,

lco" r * or

sin2r = 0, fzx=nn,neZ, i

x !.nh.k.Z.

AITEEPA Mep3reKA. r. ra iH. AKaaeMi{Hrt piBeHb

lt!

469

cos' ,r

1 + cos

- sin'

2r -

2cos4xcos

2-r +

fos4x=Licos4r(2cos2.r+t) .,

l;x;;:; n,n!.n-z. I n nn lx=B) 4.neL. t-" e q'. -. rt'2nh.k(L -!':t nh.k(z1r' lx

" l4x=-21nn.nLL. .t cmzx= j;

=.,

sinSr = 0, sin. cos3t = 0;

2sir 3, cos 3t = 0;

lon

flx=nn.nez,

l"', I

,,1

\2 ","{r

l'"*[* ;)-" ("-i)=''

= o,

!,S,n.z;

sin2r + cos2x = ."E"i"

sin2rcosl+cos2rsin|=

l* Ir 12 -n.on.n-2. 8 I

f "inzr+f

47o tii

S,nez.

2-rcos4n

r, "o"

"i,'

o" = 2sin 2.r; sin

sin 2,r = 0: sin 2"r(2 cos 4x

l'=+.".'. 'l

l3v rr r +nk.ReLi ., _+_= 242

1) =

lsin 2.r. - 0.

lr_"0,_r

=0,

l,=+.^.'.

=,!31t22 - zn*. * -2.. l, =, L -!!. o. t. o.z, xL12+4. * ez. 2

3 l, 2 r x-2

5 3 5 3(x 2\t5(x t 2\ x-2'x-2 x-2-"' lj.+2)(x-2) -"' 8.r.- 4 8.x+4 31 6+5r+10,n. - Ifsx+4=0, ^ tx -2ltx -2t tx+2ltx-21 tx-2Xx-21 [(ir-2X-r-2)+0i

iH. AKaaeMi'{Hl4i

sianouiao,

->o: -2, -!]u o, t *t. zl \

-=u:

(

2 2 A 3 .n. ztxr5) 3(l 2-r) <^. o, -' I 2x. .x+5' l-2x _ x-5-" {1-2xxr r5) --' 2'+10-3+6' <0: 8r,? lS.r-7=0. (1-zrxr{5) (l - 2.r)(-r + 5) l(l - 2r)(.r - 5) + 0: -<0: It --i\ /'-:\,-i\ /- J'= s' 57 1u 8 2 1,,1,,*r. l2

.hLz.

6x sin2x sin2j

l-.

2sjn

n+2rn,ncz,

AITEEPA MepsntKa.

ez.,

","u'=r-"13*z*J; -

s65. 11'x+2 -l2

L 4 .n2nh -;'.kez. Bidno6i.Jb: ;+znn,ntzi ; 5.) cos' x , cosz 2.r. cos2 3r I cos2 4.r: l-cos2x l-cos4r l'cos6r I cos8.r. 2 ' T 2-t 2 2.os 3' cos r 2cos 7t cos .! = 0: 2cos t(cos 3t - cos 7jr) - 0; 2cos t zsin 5r silr. 2t = O. 8

&F ? = r.r. 2 3-1

cos2r=sin.t;

2nk J

!!,

"t'' "t"(r,ni) "t"' = o' n [,",:_lJ n Ir| +-=nn.neL-

l:' s,, - Itx=-1n t ^ ,:::"nk-hL7,: L2

Bianosiab:

f,+rm,^ez

,.r.[l*ll-"l.'"*ll - I \2 2 8'"""r 2 st=0, L"*fr;_l -"-..{

,meZ.

BiAnogiAb:

'=!.,.2. lr, "=nu.o.r. l, ;-f;.r,t. l,'i=;'"^,..2, I' i rm.mcz. 4\

sin 5.r = 0,

Lsin2r = 0i

2x=nn,neZ,

l,=+.".'.

T,n ez:

]

La!!.16y.

3) cos 2t - cos 4]' = sin 6t; 2sin.r sin 3r 2sin 3t(sin t - cos 3t) = 0;

Bianoliab:

BiA6ip rcopeniB:

+ cos 4t + 1 + cos 6t = 1; (cos 2t + cos 6r:) + cos 4ir =

si3n66166;

1 lrcos2.r I cos4r*-I+cos6r' I 2 =2i ;: - 2 --Z 0i

cos" 3-r

Bidno'idb:

piBett ll!.i:iilliiiJtl;i

l',

l].-1 i,

--l

::il::i1:$:i:,jt:l AITEEPA Mep3ncK A. r. ra iH. AKaAeMi,{Hrai piBeHb

!lt:

866, ,qns po3B'nsyBassa

..5 '7

I cnraB

vxr

' 7"

x+Y=28

!'+!,=tE 7 7'

crnaB

Paaonr

[x=2a !t, ze-o ll'.1,='n' J177 *so -,n. t40 -Ua +aa _u. tno;rn piBsssEs:

fsina-r+cosar -

Po3B'fi )ri€Mo Apyre

s=zr,

y=6U7 =zt,

=rn, zo

2-! =t 7

y = 11y a,:

lc = zt'

rr - II cn;rary. 867. sin r + cos r = 1 + sin r cos r; 1=0; siIIr sinrcost+cos, sin r(1 - cos t) - (1 - cos r) = 0' (1 - cos t)(sin , - 1) = 0; T-- d-- , t-cos.r=0, lcos* t, rr=ztrn'nF7' lsinr - 1- o; lx={ .2nk,hcz. BiAnosiAb: 7

Bi,q6ip EopeHiBr

cnnaBy; 21

€2 .

lzx

f,+

Ar.rB.

n*, * ez;

fifih-

cos .r = cos

40"t 2

;

(eoE

20'+ cos(2,. { 20")) cos4o"i

20'+ cos(zt + 20')

t2)

472

z*"s'; |"lna,*fcos3'=cosbr;

i cos3rcos f, - cossr: coslar-iJ -zx-!. g*-! -2sin 226sin 6=o: ,"t(

sin3rsin

-cos5.!=0:

t(so" \2)

cos 2.r +

sin2: = rD(cos'2r - sin'2*);

(cos2-r + sin

2rl(l -

V2(cos2x - sin 2.r), . 0i

- o. v2(coszt sin2t)=o;

tcos 2-r r sin 2,r

lJz I

cos(24 + 20")

atanoaiad:

l+=-.r,-"*r,.

= cos 40'i cos(2t + 20') = cos 40'- cos 20'i = 2 sin 30" sin 10"j cos(2t + 20') = -sin 10'; 2, + 20'= 1(180" arccos(sin 10') + 360"4, n € Z; 2r=+(180' - arccos(sin 10') 20' + 360', n e zi \ ; = 1l 96' '-srqqeslsin tO't - 10'+ 180' n, n € Z.

cos

+ Ja cosBr =

,ne

r-rc2.r=o,

prcysoK.

^fifihBlonoetob:6+n',ReL.

2t 2coslx t 2o'i

+ - #+ f,

cos2r + sin 2r = Jt(cost 2.r + sint 2rxcos' 2r - sin'? 2r); (cos 2r + sin 2r) \E(coszr - sin 2r)(cos 2t + sit2al =O;

1tn

lzx=nn'nez'

BiA6ip &dpeEiB:

2) sinBr

f,+nn,nez;

a7.

-2sin 2t cos 3t = 0;

fcosa'

Bianosiab: err"

+2nk.heZ.

cos 2x = sin

= 0, = or

lsin4r+cos4x=1.

"in,=r; L2

5r; i(sin x ' sin 5r) = sin5x: 2 sin a + sin 5r - 2sin 5x: sin t - sin 5, = 0; lsin2r

L - !- 1Y. 16 164

4t;

arB. ptcysorc.

BiAnoai()b: 2nn. n

868. 1, sin 3x

I 0t lsin ar r cos4x.li

.i"a'"""I-.""a'.inr 1, -L"i"n',1.*n'=1, J2J2J2nnJt "'"(*-lJ=#, +,+f,=ttt'!*n .,€z' 4' =( D"f,

lx+v=za.

MaeMo cucreMy:

!-et

S69, 1) sin3 4r + coss 4r = 1 - 0,5 sin 8r; (sin 4.r + cos 4r)(sin'z 4r sin , cos 4r + cos' 4x\ = 1 - Eirr 4, cos (sin 4r + cos 4rX1 - sin 4r cos 4r) - (1 - sin 4r cos 4r) = 0; (1 sin 4, cos 4rxsin4r + cos 4a - 1) = 0; (1 - 0,5 sin Srxsin 4r + cos 4r - 1) = 0: I - 0,5sio 8r = 0, I sin Sr = 2, I ueruac xopeaia,

BaAa.{i crina,qeMo ra6,1sitto.

] *""o",",n r0")l

- ro' I t8o' n, n cz.

i.l,* ,'IiIIEEPA Mep3reK A. f- ra iH. AKaaeMi.rHran pieexr !ii:iiff.;..;.;!!i

a) 1+ ts 2r=0;

ts2x=1; 2z=-!+nn,nez; x=-[+l,nez;

6)'J2J2J22 cos 2ir sin 2r-

| ; *"o"

z* -

*"tn

coslcos2x-sinlsinz'=1, *"lz'.')

zx =

t!-

znn, x

fiItn ^ Bi0no6i0b: ;t

ez;

z = tfi

-[+

z* = 1;

r' ! 4) 2 2, , 4 = -\3 * z,*. * . z, n*, n ez.

1l 1r _ ,neZt !:-:+nk,kcZ.

ilili:i:tjlli-itiAnrEEPA Mep3rtKA. r. ra iH. AxaaeMiqHxi piBeHb::it 473

azo. 1') 2cos4:21= x,

2"o"t-!3a = 6

, r,

- 4" *

2"o,t !!1

5) te,

," ,, 4r,, 4,,2.

-2)2 +

"o"t1?' = !r'+

t <--

tsx>f

+ ,tn, n e Z.

piBBrEEs Maâ&#x201A;Ź RopeHi,

" Mae KopeEi,

"i.n14-

rKryo

(t -

4r * n+ 1; "" 2rz = O;

sin 11 =

(r -

2), +

;

[+nn<x<!+nn,rez.

= 2.

7. Po3B'r3yBaHHr Haf npocriulrnx rpl,iroHoMerpr{Etax HepiBrlocyefi 821. r) su.t

]; -U+2nn<r<!+2nn,nez.

BiAnMiA6:

(-!*zn,t!,zn^\.o.2. \trtj)

Z) si.rr >

-!+znn<x<!+znn-nez44

-f

;

-!+2nn<x.s!+znn,nez.

|-!*rnn ! cos

n ro,],

n.t.

t; r 5 J9;

n l7n -+zfinSx<-+2fin,neZ,

BiAnMiA6:

(-i,2,,,! * z^1.,.t. urespl

BL0noqidb:

(x z l \ -+nnt- +nn),nez.

Bia,o6ia,,li +ftn;-+nn).neZ. 8)

?) ctgr < \f3; n + in < x < T + Itn, n aZ.

ctg t>-1t

3r 4

nn, n eZ.

BiAnosiAb:

l:i!i

-l;

+ nn <

BiAnoqidb:2.

a7a

nfi

-2.

grn!1 =

piBEsEss

4r + 6:

=o;

"*uo |{,+zl" BiAnosiob:

+ z)"

BiAnosidb:

f;, r^,t!t n r^,],,.t.

Mep3reK A. r. ra iH. AKaaeMi{r.nr pieenu Lll!ill{:!ili.:;!

-Bianosiab:

9) sinr

lt+

n.z.

+ 2nn

<.r < arcsinl

-|+

+ nn), n ez.

> 3;

nn <

t <|+

no, o

ez.

+ 2nn,

BiAno6iAb:

Bi0nosiAb:

(-,, - *""in

sianoaioa: (trn:

10) tgr

;;

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thi n* n,).,

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l-t+lutt+nn),nez.

;i:llilillllilii

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iH.

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BiAno6i0b:

144)

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lsn - l | -+ 2ftn.' +21tnl.nez.

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zon). n )

(nn;!+

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f,+nn<x<n+nn,nez.

aianoeiat:

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t; '3 nn<t<-+nn,

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10) cLgr <2i arcctg2+nn<t<n+nn,ne

2n,

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". ur *",f; * zn,,

Bianosi1b: (arcclg 2 + nn, fi + nn),

(BiAnogiAb:

BiAnoqiAb:

lL*z^.,4*z^,].,.2. 3

l-:*2"";:*2"")'".2

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l--+nn:

476 iii: AnTEEPA

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)

Mep3nr( A. r. ra

iH.

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;

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a+2

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;

t, 4x-12>o;t! 6 18r l{x) =

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l(,)=#+L

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488

to4 =

r::.j::

5=:

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f('\

= 1.

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2; E(f\t

ATrEEPA Mep3ncK A. f. ra iH. AKaaeMi'{Hr4i piBeHb

|ga.\ f(4=Jx+7; fl")=o; G+z=o; r+7=o;r=-7i - = r"+4x 5 /{x, -. Z) /l,rl = ui -:lx,,ar S 0: x=_Sa6on l; +4x_5 I x b:_ =(l: ,r-l [x-l*0: lr/l: e1 nx1=uQ at fl')=0; rt' 6=O; x' a=o; r"=a; x=xr6 t?

f @\ = (x - s\Ji-r t(')=o; (n-s)G-=o; x-3=0: Ilr=3: r=3a6oJ.=4. LJ'-a=0: r=ar

::i:::::::::i:::::::::::i:

iili::ttii:;lil{i AITEEPA Mep3riKA. r. ra

iH. AKaAeMi.rHrn

piaexs lf:i

499,

[-9,o*,qo*<r; I.r frr)= j-x 2.sKDro 4<x<2i 8-.'nqojr>z.

895. 1l

2) flr) = ll

4) /(jr)

= x-2,rpsMa;

6) l(r)

e) l(r)

.inep6ora; 8

-2

-1

-0,5

(-*;

411€

spocrae IIa

l(r)

lz'

^) 6)

u*qo

sal2; +*); l(r.) crana€

fs.rxuor<-2: 2r ftr) = lx' - 2x - 3, n.Rrrjo -2 f(,,

3ararbEoro Bnrnsayj l

[ 4; 2]'

< x < 4i

= 5, npsMa lapanenblra o'; !) 2x- 3. napa6o,ra. {Birkr'r, eKor

^x)= Bropyi r'" FarpaBned

=: = t u"=1-2 3=-4,(1;-4lt 0

v B)

l(r)

f tx) =

fl)ct =

0);

+-).

= ,::

Dlf\"

(--; -1) u (

€

11 ! '

-);

!l!

1; 0) u (0; 1) u (1;

sifl

3r ( :.\ + t= r' r-r+liibvHKqin

I x)"+21 xf Gr\" - 4( r)

x3+2x'z x' + 4x

iftfl

rry

I) / oi

+-);

(*i 2t w (-2; 0) u (0; 2) u (2; +*); tr" 2x't | - 2r" . ovHxtlls ^ G' ax) r'-4x

Bpocrae tla

/(.r)

[1; +-); l(r) cnanae Ea

[

2; 1]. 9O1. 1) y =

s>o; Jx:5: ee6. r) l(n)=1t-+tE-x; o(ft: lr Lb-.r>o: lrssi 2) f(x\ = J-r' + '; t<O;x(t 2)<Ot D(f\i a'z+t>0it'r € [0; 1]. 8s7.

(,6; *

D(fl. ic& 4x+O; t+Oi r t!2i r

3, npnMa;

f(r)

-3

rpr a € (-2;

111 i HPnapHa: '/{-r)=- r.Yf (x) x'+x 7l f(r\ = (x - 2ll (t + 2)" D(n: )e e ( -t +-)i f( :t) = (-:. - 2)l - (-r + 2)a = ( Q+2)ra ( (t 2)r1 =(x+2)4-(r-2f = - -((x - 214 - (t + 2)i), senapHa; 8) /(r)'-'l . DD:Zx+6-0;n=-3:.r=( -: 3)-( 3r -): ,(n He c4MerprlrHa BiaEocEo ro.rrcr O, i(r) ibyE&rrir saran6Eoro BlIrrEAy; 9) fl,) = r3lxl; r(D: x e (--; +*); l(-r) = -(-,.f-t = 13,r, I]erapHa; l0r frx)=+; t' 4t

> +.

nKqo

= a Ma€ piBHo oarH l{opiEb rrpz d € (1;

s) f(x)=\ls-"; D(f)t I r' > Ot 11 = -3; r, = 3; r € [-3; 3]! f1,1= nG - 1-ar = urg ;, ".o"". 5\ f(r)= x' - x +Li D(f): r€ R, f( ')=( ')'

-9,

Mae xoqa 6 oanH Kopisb,

= 7ic6; D(f)i

l(r)

". (*; - "6). (-"6, l5),

Or), 2 I(o'

2) fG) = 3r5

0,5

t i ( -; +*); /( r) = 7( r)t = ?,6, rapEa; - 2r1. D(|Ji r € ( *; +*); fl-r) = 3(-'f - 2(-t)? = 3r5 + 2'1 = (3r3 2,?), I{enapl]a; z) f(i=+-; DU)t',-5+ot x+):.15;

9oo.

-16

l(x) = 0 (ro.*ca reperrHy

a e l2i +*\: 3) flr) = a Mae aBa KopeHi

Lu1 1'1 = -9, "l,,"Poo,,u, g

pesi;

Ji1:

ft:

""p""

y, t

!:!.

r, a OyEXrIno - qepes y. MaeMo r-g aoo I r. , Qysnqrrc r= 3 v=t,r ^ n ro3'a.rr.rMo apryMeHr t, , Brpa}HacMo r qepe3 9: , 6=!;,=!*e. g , _6, s fiosEaqliMo

trcpe3 .r. a

'at:

I Lgxrrox<2:

U. EKUro 'r > 2i

ftx) x:. nxuo D{/r: (lt.E). ro E(n: {l: 2r' 49O il:::AIrEEPA MepsneKA. f. ra iH. AKaaeMi'{Hraf

3t + 9; B'rpu*""to t

3,)

piBeHb ::::i:::::::i::::::::*:::

oaepi*ranifi QopMy,li apryMeEr.repe3

OyHxniro

1,E:n

2.rt

iliilili{iitil

qepe3

g. MacMo OyqK(iro

(ArB. nosclevt.r ao saBAarHs 1);

2x r.u..,=1_1,, 2 2" ',=1_1", 2 2

A'TEEPA Mep3rrK A. r. ra iH. AKaaeMi,{Hri piBeHb

ii;:i

491

a=2-nli-4; nE-1,=z

'-4=4

4g+a';t:=g'z 4v+8ta=x' 4r+8'

5ts x'ixc [1r--)r x= Ji, v'"G. 6)a=xu;ze(-*;-21; "=-Pli; u=

l(r) Mee €AllHuii xopilrb Bi{nocso 3MiIIEoi t, ro rBepanieEEs npaB[nEr{e. 2) TaIl, oclcitERv piBlInHEfl y = l(t) Mae €Alsri liopiEr, BiAHocso 3MiHHoi r' 3) Ei, ocnir6rcr.I piBHnnna y = l(.r) riroxe uatlt ABa KopeEi BiAHocEo sMiEEoi a. sara"lrHoro Blrrnaav. 4) Hi, y = g1g 1- t.rapHa, y = arccig t - OvHrcqis Ri D(g\, , € RtE(itae n; c={;; D@\ 5) Tax, ocRin6&{ y =

9O2. 1) Ocld,'lbftr piBEsItEs y =

+6\ c=!t,

D(g)t )ee R.

9O3. 1) (2t 3X3r + 2Xr 9) < 0. nocniAoBHicrb po3B's3vBaIIIIs: 1. 3Eafrrn o,43. 2. nepeHecrr Bci q,reHtr HepiBuocri BniBo. 3. fiprpiBEsrn niBy.racrxHy,4o Eyrs i sHaiira ftopesi orpnMaEoro piBssHEs. 4, Iloana.rarr.r orp&Maxi qzcna n O,q3 IIa qncnoBiii 4psMii. 5, BMrsaqurrj BFak Oyltftrii Ea xoxHoMy npoMir{Ky.

6. Senrcarr OA3:

Bi,qroBiAb.

€ fi.

,1.

+ 6)(, +

2Xr

4\>

0i(r+6X'12)(t-4)<Ol

O,43:,'eR.'

[,r+o=o;

492

r:i!.:

(r-ll)(n--4) lo; o,u3:.r r-1O

t-.1-11)411) = e, r-10

fr+11=0:

Ir=

"'!

10 = o;

(, rll)(J r4)

-0,8 r

--a,ti\'-\T.. r

rri

| 11;

4l u (10; +-).

(.r+6X"r-8)

6t{r

-11 -4

lr+n=or lr=-1. BiAno'iAb:

o,4

= 10;

8) +

* 0, 'i*a -"'

(-;

-6) u [2,5; 8).

-!*'1'o;

rE,u;

o.zl3:x'?r6.r

lx lx

+ -2.

x'z-5x+4 - x," _ 5x "" - + 4 = O; x = 4; x = 1; -" !=0; (.t 4Xr - 1) ^ (t+4\(t+2\

(*i -4) u (-2; 1) u (4; +-). 2l^ i '^.O: OJIS: .rr - I - 0; .r * -13. xr 3x' 2x 0: xq 3x, .t 2x Oi xtx, - 3x + 2) 0: xt= = = x'9

5)< 0;

ffi

'!'-])'-!\.0. (,-3)(r+3)

4,8 15

4.4

r 7,2=0ix=1,2. ( -; 1,21 u (8;4; +-).

= Ol

Bilnosi.Ab:

5x2

Bi0tuosiA6:

t'-u

'15x 2 o, ':5x-2 2+OixxO,4i o, 2x r r.6 - o: -r = ,0.8. ( -; 0,81 u (0,4; +-).

BiqnosiAb:

z--61

2)(x 4l=0: lx+2=0: lx-4=0; BtAno6i0b: (--t 6) u (-2; 4). 3) (' + 4,8X1 - x)(5 - x)<0iQt + 4,8)(, - lxr O,4B: e -8. ' (t + 4,8Xr - 1)(t 5) = 0; lr++.8=0r lr=-4,8; tt lx-1=0; lr=1: Ljr 5=0; Lt=5. BionosiAb: F*t 4,81 u [1; 5], at j-1220, o.[3: x 8.4-0ix/8,4. -_"

4i l'6

On3|

?)'

1]]4 2-5x s o;

so+. rr'x'+6.Y+8

I - 3t.i\ tz ; 2)(6+r)(r+2X4-x)>0; (' {-r+6X.r+

BiAnoqiAb:

la'*z=0, l*=-f, Lr_e=or lr=e. ?f

x-2

r -&l- = 6; x - 2,i =o; x= 2,s. (r+6)(r-8)

i'=r.r=t1, 2 lzx-a=o: |

IJ36'

BiAnNiAb: (2i 51.

o-Il3: t.r +

Qx-a\(\t+2)('-s)=0;

niaoouiao, I

6, -1:!r6, r-2 OAg'.x-2+O;z+2i

I:!=0, r-5=o:r=5. x-2

\G-

'3, Elgl DIV\' EG): e c Ri Dlgl ElCl, = 6) Hi, ocni,rrxa y =;rat D( tt.Ii;t(y):[0i E(g); t0; +-); D(y) + t(s).

' !:I2 r-2

AITEEPA Mep3neK A. r. ra iH. AKaaeMi'rHrr piBeHb :i1ti::rj:r::ii;:{

( -; -3\ u (0; 1) !-) (2; 1> 1, o-[3: ,r + o. s, , *

Bianoeiob:

W,B

3).

x2=

Ii x,=

''1 32I'o' D=9:r

2x'- bx-2 >o 2x,-bx-z=tJ;

x^ "22x

aianoeiat:

ttillti:jliiliii

.r:

zt,-zt( '

!) z':0.

\.TY=Y* 012^

(o;!)wP; + *t.

AITEEPA MepsrrKA. r, ra iH, AKaAeMiqHrfi piBeHh

tltj

493

$ 4!J 3y, oAB: , * o. lIf 1-r.0. 3'+1-t<0. xt o"'=o;2x+r=o;

gos.

2t+1 _<{).

(.r +

-)€-]V-. -t10

51 1 __2>Ua

BiAnMiAb:

+ o.

{r" -1lsr-?. x I

lr:

o.[B:.rr- l

(t - 1r(t' + t + 1) + 0; t + 1. x' 8 r.r'-2x2+t'z 2t+x 2l .^ --- +Su; (r-1)(J'+x+1) + 0t

6\ 1)(ir' + .r + 1)

4-r?-17.r I {x

l)(x

l5 ,0. 2)

o; oAB:

3)"

.r. , + B.

(jr + 2){x 5) ^ ---:------:i- = vi

s=o;

(r+2X,

5)=0;

;:;:.!:.$

l'=r.

l-2;3) u

(3;

::::::::!l

51.

(x +

l2x + l\'ztx ,r"(r. +

I)'

o: o.[3: x . oi

' t

r\ /--:\ ?.--\/------.----+.---------.#

z [el 5

t3 -4a'z+3t ^. : :- 0; 'r1 - 4r' - 3.r = 0: r.(.r' 4xI 3)=0;rc=0:r=1ix=3. r(r 1)(, 3) > 0. (x - 2\(x 3l BiAnoqiob: t € (0; 1) u (2; 3) u (3; +-).

-stE- .o. oo". [z-t:o. l.z. 2.x t3 [x/ -1.5: [.rr-1,5. r"-st"E-_r. r,, cr6: = o: x=!3;t-2. 2x+3

11 4

1;'+-2. 3 ^ ^ 2lx t 2l -3lr I) 2l.r + l)(.r 2) ^ 2 (rrl)(r r2) x-I r'2 2x-4-3x 3-2J( -6x 4.n -2r"---!' 3,6, 41L,-3 ,6, (.ir - 1,{'( 2} l"r - l)lir ' 2) lx JJlx t 2) ' 2t'7rx-3 -.o:2!, x 4=otD 2si r,"=-l+5i t.=21 t" {x' IXr r 2) --

('-3Xr+3)J2 BiAnoqiAb:

r,s.

:a:a:;::i::::::;:i:::ii

>0.

FB, -r,5); {2;

-\-a/1

z t,s z 3

16 r' (r+r)'rE+3.0. @ q@+4)

3}.

,, rl;'$ a . o, ,, -,1,_fE . o, oo", I _1. {i rl-llitlr 3 o, r, rf,/i-3 = o, [' , -l'

BiAnwiAb:

11.

Mep3reK A. f, ra iH. aKaaeMiqHlrn piBeHb

jl'

2r+3

2lx-1)lr.+1,5) -^

1,51u (-1i

g06.rrrr

u 2-+4;>z: o1gtr*

494 lli: AITEEPA

|E-2br

e2,5r: \-3]..

(2r+1)'('-2\ ,.. frz'+rf =or ,= ]; ' f*-z=o: ", " r'(r + 1)n "=, BioflosiAb: ( *; 1) u ( 1; 0) u [2; +-). 6) '".41"-g'o: oA3:.r'z 5r r6/oi,r,2rx + 3.

6 0:.r--3:"r z.fl111\C-

LaL.a, on}i x+Ii r+2. 7, x-I .t 2 2 3 -- 2tx-2\ r3{r l)-4(r-lxx 2) x-l x 2 {r lx,r 2) z'__1_fL Q:4l1t2x -8 <o. 4-y'/r l7.r-15<0. (.r lJ(n - 2) rjr l,lir - 2) 17+7, nr I r 4x2- 17x I t5=0:' 49: =1-i ',. =- ; al' \ - r1)t" 4/ ar ,O. (r. lxir - 2) * Bidnosiab: F*t \t €(r ], z), ra, -r.

C2t

+Y-+\a:])/'+

* 5 o.&3: xt 2ix."-8. 2\(x 3)'^<oi ::_=o: j 5=0:.r=5. (x + 2J(x 3)' Bion%iab: ( 2; 3) u (3; 5). at

1)(r'?+t+1)

(r+1)(t+2)

13 -i"'-;

5).

ql?+

BiAnosidb:

, '.,j ", 0:ir,-"r (.r rJtir- f.r r i) Bidnosidb: l--, 3i '(l; 2|.

BiAnosiAb:

+V1\(-::V-

fr+z=o: [r=-2; ->ui

r3-g x 2 <U:(r 1Xx'+r.+1) r 1 ," 8 t" + 2x' t'+%c-t +2

- 311

5r l2.x _>U.

(::

F2,

(arr3. trorclleEEn ao saBAaHns 1).

"f;'=o, r,-r=;, '=+ s;anoaiao:

2Xx

tr*3f .0 z, (x+2)(x-5)

)

!! Jr-2t oAs:

2: x

(x +

BiAnoqiAb:

e;a",,ia", l-1, o). t1

'3t' oi or3r ir r 2\(, 5l (r 3)' 0i tr J). 0i -r.

lr=.3.

"4 (:\(34. 3 FI 4

3; 4r.

i:l:ittiililiiitli AITEEPA Mep3reKA. r. ra

iH.

AKaaeMi,{Hri piBeHb r:::i: 495

3, CreneHeBa OyHxqie

soz. 1) 4(-i6)' - t,.vm.o -

[i ltto)' = -20

0,6.10 +

3) a=\tlx-2)

+.640

q v-{a4;

D(y):reR;y=lx-21.

D(a)tt-2>D; r>2tteL2i+6). a=t-2

=-2O-6+40=14i 2) 3) 4) 5)

n[, -1".t; 6) 1lJ2 =

"56-

= 1n =

{12 2+2$

I,lltz

t +

J2 =

,Er

srr. rr

{:,z,fz

(

-,rlq;,tA = O -;AWn - F - txil 12

ira - -2.

909. 2)

.i6;

= J"l =

srz.

i/3"-sr D(y):3.r - 5'0, *>r3, relrrt+1: 4 a= -t; D(Y)i-,>oi/'<o: 'â&#x201A;Ź ( -;ol; 3\ a = 4!x a: D@ri x e (-*; +-\t qt v {6, . lt Det.6x x, zoi xt6 -.r) z oi -:G/0 -r-0; .r=6:.rc [0161.

gog.ri

- :

o, s*qo a > o;

tltt =lo = -a, slcqo 6 < o; =ls^^"'pl= s^'""p, 'Krqo n < 0; t,u"Jira"^ = t, t"lz"'l = -2,arn , snqo r 5 0;

{zt*t*i ,68"-

b",.e*rqod-o,c<0. "b! =Uttl abc abc zl y=trG4; 91o.\ u=llx-2); D(V\tte(--;+-): ,(r):re(--;+-); 6)

-.,F)- -,lz =lz-,111-,lt -

i,[rtu

-" = "'tF

d""

ah.

d-zney'

ll."o"

d-ar.

= :1"'"

z-Jz

""W

= o%\,lo"r"

5= rr v4 = v43@= .i/2-sE .2 v8-stlz. 12 12.li tz.dz ,,1.. ". '' E-ffi Ts--W - tz.tE s -"'"' ,, g=94=s4=fia,

grg.

'V8 {az 2 ,, 14 14 V7 :.41,!i .xE. ! 4s { 4s.{7 7

s(a*f) s(a*"El _ s(qtuF) _^*,r. ,' 4 e. s J7 14-h)14 th) 16 7 (Ve' r .. "' {a*{t (17tI {6'Vr) {6 -.f6_j[. z) ^ 6",_ 2 ts

'' ATTEEPA Mep3rtKa. r, ra iH. a(a,qeMi'{Hrr piaenu il!*:ilfl*it'ii:'r

sy1 - zy,!-zy:

-(q,E)'

496 lll

uI=t ,6s lJsb-d=z-.6b+JEs-e=r;

ff'.fesf xF

zl v_a' = _i6".a = _a'16, il 1862*-j = 418L2*" *"."' "" = z*"o\li^"o" Et rls6;W = {ir a'- . ," . om = zry'{iz\;

3) 4)

t, i/{z

plzs

o(a , zVt

lt '

'.Vzr)

o(l - z'6 .

(r/t)" g(S*r)

(Vrs

:ittilft:r:*l: AII'EEPA

rX",,6

Vzr)

zlr t z{s . <!zs):

e('6-r) e(t6*r) a(Vs r) (vb)',r, 6 - 3 'r)

MepsfleK A. f. ra iH. AKaaeMi.rHran pieenr ilil1

497

gra.u Wa =iE 3) nAG ='vc' c .

2' flE{t' = {t.'t"

a =4,8;

='d"';

=Je;

sl f6ri0 =,Sls='ne. gts. rl i6o . {6, .""i"'""

*lzJ,

=\lt = Jz; =42* =42" = *lr.

Va) _vo nru.,, Jg Jg_(+6-16)('6,' (V"

.. s[ z

Va a

1i7o

+ Va)

(J"-r) -

r;1go *

Hn :1-=

='F.

va.

=(ri -

n,n.

31'.

o?.3' { =

nâ&#x201A;Ź [

1;t=7;

494

lltrespl

b,\ol

\a!-aaba t

\a4\a4

,i,

+u)

a-,

=(1J'-(*)' (9'=

11!l

nL1

'z' l

. (roi)' - 5 - 1 + 101 = 14;

wtepsncKA. r. ra iH. AKaser,ri,{srr piee}tu

n1 = n1 _

IoBeAerro.

a-b

otb oa6t a6r t\l 2

aa + a,aba

oi-bi +ba aa bj

la; _6,](a; _a,b; I b") -

t,r

\,,

=at +bt

r\/

+b3

\o', bs

1,, a,ll,'

_ o')

""t, rr1111111!rr _as _a3

::llfilillili{li

^,1^t,^),t

I l =m -nt

nr.

2) Copouly.Mo riBy qacrnsy roroxEocri:

oZ - 6,y,, -

I / n -n,'\ (n\' ' \m-n-n+n"n"ln'

l '--'\ \n'+n')

olo,,

rtl a' t b1l)

(,'i_";)(,"r.":)

(V*)"

256arh,

l;:;; ;.f,,)r^'

" ,] l(,1)' , n-l llr",e,r; -(,;).J l(,1)'.,. ,= lll:

AB)

I o,b, I b, I a)l-l-

I ^ ,

=19*64-1=3*64=62;

, ;

25 l. ".10 I I ",2 3 3. .1-* / r -rL o, (o,ozzlJ +zse'lts'iJ =(0.3'r"^ 2so'5-ir=o.a

92O, I) Cnpoqycvo,liBy qscrHdi roror+(Hocri:

sy o,rzs i+o,sri-0,216-,? =1o,sy'+10,s)-'-(0,6)'

;

t1tt "nrh,

3r'o'

=3i

-(.*"" t)

,,0,

on.

,,,

+-);

uru"""

,jri,rr , t=l__;;,,r,lu;r'' ,1, ,t\+

'c' 625c'3 l"Ih: *"trb:]" l,ib;(,; .b;)l'

1:!1 2l tl 3.11 4 .11r, .11 , = 1. 121 3) 360r'6-01=6'{.6 4r ::=a=3r

ft = fi

- r'") =(rl" - p-'t"

3 3\3 125a'-h'

2) a=xa3t Dtlt: x oi 3) u=(r+ 6\'6;D(A)i:r+6>0,t >-6;

918.

"')(ri

l a ll '- rg'r l a: - s'; 'i i"' 'l ', ,u"J 7 e'ti, 27'

-6t-7)-6t 6x-7>O;x= re ( -; 1)u(7; +-).

\la +2

., \!m"= \!mi

9't7. 1) s = x6l, D(ar: x > o;

y -(rz D(y)t ?

l':-i.,ll"l1',. "-l;l',]=

1""",^,',J

r,!,

[3r_(1]'j(s:.i;l l={,,r lIj] l' ( rl '' ,n, t 1 l { ni i,Er [r: -titlll(r; ' '"' lf-n',, , tL""'e "'" " r I ' J'- '-'"' 'l l- ' \ 2t 1'' -rl;)=

^-tl^" Jn tn tln\tln r) 4.lV +etli +s {V *e{" +s x-27 = (G ;nV-, :V, +o) = if-, a' <1,,t

Isl (o.sq/o.i)"")lr,'"

= .Vsl;

'6 zt Jo . .,6, oc&iJlbru i6 = i6e ; Ji = rll%l al l/il r ocrin*' ../5 = 16; q\ {n, "6, 1E,.""i"'"" .'Ei = lF='itr, t/5 = i/d Va +

/,\ l(r;)"-,il=(r,_rl)(, _s))=2,_s =1 i_

=:{t";

=bt

ta,bs

r\/

+bsl [,'_a"J(""*a"/

I oibi bi)

&3. br

:::::i't:iilijf.!i! A'rEEPA Mep3nex A. f. ra

=Da a3.

AoBeAeEo.

iH. AKaAeMi,{Hlri piBeHb ii:::

3) crporqyâ&#x201A;ŹMo niBy 'racrlltlry rorornsocri:

I s

).lorr8d3

a3t2

fd+8 o;

2j, -a) 1l aB -2

nepeBiprcai

5 d3 -

1-oi r-ai

as+z

oi -qotr s-oi I r\ (r-oi]tr *,iJ r', o; 5 = 5. AoBeaelro.

4) CnpotrIycMo

"1iBy

sol

,3 -rol

, s s,? ,,

2 = 2. flpaEhnbHo;

1Er"

4+2r-x'-r'

=z-z;

- llt- tl

2x2

r+03

BiAnosiAb:

2, ls.e!pasuntiflo; z"=3:

L4tt

+ 13 = 25

;a zy u.{-2)-13 =?:

rE.6"L4'6 +14=-1;1=

^\' I,

'i)(qi ' ^:^I '^1\ I L\

/ r

1Or

a2i 12

- 4t -

? = ?. rlpsB nEsor

12 =

x, = 6:

-2.

Jr-J''-ir =x-tr r-uG' I =x"-z*-t; '[7 -," =z* '" 4IJ - 0i.irr =0 a6o

,"=i=tti

=0-1; 1= -1. senoalsftso: r.^'4= 11,

f rs r i

"^:^'"

.iI--=-:

\16444

1, HeBpaBHnr,Ho.

IlepeBiprc&: .r, = 0:

)

{,,r ,:)

I I

1= 1, rpalrrnbno.

xt x?.4x2-4x6+f 5x,-4xx=O:.rr(5

(^i

x, =

4x+ 4;2x2 -6t= 0; 2r(r 3)=0;

rr =O: Ja+Z.O-O=O-2;2=

nepeBipxa:,,= 2,

-,;

(,t-,1)

BilnoerOt:1!.

6\ =

)

=2t 'li+Lt=2+Js'+7; t+11=4+4Jiiii +sx+r: t1li7*; -r=Z,,Er+7; x, = 4(3t + 7li t, - 12x - 2A = Oi

'li+i-Jui

-2r =

fiepeBipria:

,"=tc:

r\' .

x,= -2t J-2+11-J-6+7=21 3 - 1 = 2a 2 = 2, npaBtrnEgo; -2; 5 7= 1; -2= 2, EerpasrnEgo.

"Ea+11-Ja2-i BiAnoqiAb: -2. 1 -,. 1

t. ffi=

,. i

7),8 - % - s = J16 + x; ./l - zx =,lla+r + 3; 1 - 2r = 16 + r + 6li6 -za-zx 6,h6tx; S-r=2fi6-xr 64+ 16.r+r'?-4(16 r .r)i

lotelcno.

64 l6x

ni \ni -nz) J+t * m = t

z-l,;

\ / c ,l

It r\' l-t -",t

"='-z;

BiAnosiAb:8.

=n,\m1 -n'l

gZ't.

-z=z

qacrusy rororkHocri:

,t .

.lE+z s-s

'\' t n' * n;n" - n; s^i ni =l^" *2^'n; * ""1-14, - nll t[ ! l]1 I ll 1l ,l' , , , , z zr' t , r \' 2 l\n' +nx)tn'-n,ns +nsl_n:l \^, lni^;_ni n;l =\n; _n;n'l

';---n "" " _^I "^:,:

aoi

llenpaBlrrEno,

IlepeBip&a:

't' h ",Jh-orJ

l',1-+ ''w^' +', l-i-". .J \,?.+nr

-a/

'[G

,)-G" ,"i"1

?\ 31 - s-ad 4a3 -4 _ 5 - a:_:!as I a+8 a+8 2 !\ . t \5_as_4arl.a'@ '8t 5a. a_4a3 z'_'--l 1-at (a+s).(t-d'/

--,

BiqnoaiAb:2.

'';'"-;-t-n (,!ffi-;

lx,=a,

2; 4t + 20 =

,c2

+ 4x+ 4:

-16=

4)(t + 4)=0;

IlepeBipxa: x, = :t

64 o:

4x,,

12x = O,

uii-zo-a=

-tzt,ET zi - s, = Jta - n;

" BiAnogiob:

Ii"peulpxa, = l, J+++m =++z;6-?,npalurbEo;r,--q, J-le+m =-q+z; ", 2 = -2, senpagr'Irl'Ho.

-I2.

ula-,+,1*-z=r; "6-i 2Jr-2=22-4;

,Q-Z=r-Z;

= 0' x(x + l2t = 0; [x' lx" = -12

u/io*or s

I a 4t 2 - 4, HenpaBa,rr,Fo;

3 = 2; 2 = 2, rpaBn.rbno.

=t-"li x

+.r- + 9;

z; s-t=r-zJt-2+x-2;

2 = xz

- 4t

+ 4i t2

- 5t + 6 = Ot

BiAnosiA': 4.

u6-i=Z'-t;6-t=gx'-24r+16i9x'-23x+ 23113 - x,= 5 = fS : xr= 2, g. ",.,

soo l{t ArrEsPA

10=0; D = 169:

Mep3rcK A, r. ra iH, AxaaeMiqur4i piBexu

\ = 2. .tE - 2 + fE - 2 = 1; 1 = 1, npaBgnbHo; s: .,6-+.v{_z = L 1 = 1, npanr.rnr,ao.

nepeBipxa:

BiA 6iAb: 2.

llillii{illtN

B-

i:r:::ilt!li:itlli: ATTEEPA Mep3rqKA. r. ra

iH.

AKaAeMirHrt pieenu

ltl:

SOr

+ 15 = 0, 5. xr3- 4-r r12 3xt15 -rr3 J,r = ----:- = 4 =0; -x-3 -=0; J-3,r 3+0: x 3 .ir 3 l:r lr+3. rlepeBipka: uffi.t=0, 2 6.!2 +1=0;0=0.

x+5+"lt-=t: ,!z'+r=t '"b-t; 2x+5=16' }nE .r+a-r; 14 sq 64(s x) = 196 84r + 9x2; ar rn - -8'6-; s\,6 1 =qx'z 2Or + 4 0; D 256i

fg2 64x = lg' - 84;t + 9t2; 2 20rt16 - x2= -. zi r,., = rs , x|= repeBipKa: ,,=2. "E*+Jrz

ffi

BiAnosiAb:5.

=4;

+ 1=4;4 = 4,

.rc(-*;-l)L{0; I'=0 -L-0; -j-=0, I r xrl l.ir. -l: aa*i,,a: _E=r.r, o, _p=1. !1+r \l r t u)

npaBlanr,Ho;

lE-4{i

5=o; oA3: '>0. 4t -5=o;t,=lit,=5t saMiga: V;=r, t>0't'z

i,t

.5;

6t,

r$[

o. -"

fr !1+r

18:

4. - - aro

U "lV-q' ' q-z'J' 2-3=0r G-2)' 2t[x-2 3 3arina: {t 2=r. ',t2t-3 O:tr= 3; //=1: +lr-z= e; x-2= 27;x= 25i ;J,-z =t;

25:3. BiAnosiAb: '-2= 2+ -!x

Lt" 2+i

g_1 .--' . t4 - i )

2+t

r-r)(8 i '?)

2+t

I{2

,ffi

. 2+

1=8

4(1 +

-!; !.

nanoaiat:

'[V -

t, -t

nepeBipria:

9: -5"=-1;

.ffi.1=0.

o r 9+1=o; l+l-6-0. t,+t-

Bauisa:

x.'

4 - -t;

-,85 -

12+tlt2-t 8+t'zl 2+ t

t+-21

'It

lt t

-21

-=u:

L1+r+0r

-=u:

l, = :'.

20 5.

t > 0.

ta4

4; x'

5 = 0; r. = -1; r" = 5. trpaBr.rrbdoi r, = 5;

3; 3 = 3,

- 1= 3; 3 = 3, npaslrftso.

xLI:r a Jralllrllr Jra ), , ,'t 3a'riua: Jr' . Bx I = r, I : o; ,,., ar ', ut n', 2f+6t=2t2+2. ") 5a1 r,=1,5, 5t - 2t' + 2 + lt 2t' - 5t 3 O; D 1; =

,r'2

.^ 4!Jn t'Iono6lob:-:---'-. =,,

''o'

3,r s

lr,=rr

3,25=OtD=22i

ttitt. t;.r'-3,r -2=ot D =lF, *.^ ", = 2

"/it

4. TpllroHoMerpxqHi OyHKr.tii

6=o;

t Heaa'*oBonl'snel.MoBv'>o; l';"="? 502 !!::: AnrEsPA Mep3ns( A. t ra iH. AKaaeMiqHrr

uE+Sr-t=1A; f +3x L=2,25;x'z+3x st Jzz vtt J'

l--1'npalurbHo

/tt

13"-r=0,

4(l + x)

8) 5J.r?+3n-I=2x +6x+I: OA3:

rxi' r -6)=0. li'-i o o, ]l-'=-2' ".

l2+t +O:

3x1

-=0:

ne 33,qoBonbH.se yMoBy

-1

4x1x

BiAnosiAb:

=g; x-o.

neDeBiDXa:

:':3.

t2+tn/'-r-6)_0. ,tQ

l.L"-r'r.

=tn?t

7, 1=3. saMiHa: k -4'-=L t>o;x,-4r-1=t2t ? ""-4,-,,8-4, 4x=t2 + l:xl -l -r-3=0:1,- t-2=O:t|=-lit2=2.

r.3aMiHa: Vx=r. i -u.

l=8

-t

vMgBv

BiAnoqiAb:729.

r,."

-).

l,*

62s.

oA3:x2o +3, 1a=0; t'= 6it2=3t -6 Ee 3a.qoBonbg'e t2O.t'z Savisa: Vr =t, r>0. Vi

o.qa:

f__ a r x-4-4x -Sr-4 =u: -32-4=O, l'r' =0: =4t 1+r 1+' 1+r 1+ r.+ 0l t.

Ire 3a{oBonEEsâ&#x201A;Ź vMoBv

Bi0no6iAb:625.

./f--: 2 ' ri .r =1,

,r!-f,=o, 2* 5-t+2-o' zt'z-5t+2=oia=st

I s22-D

.E vlrr

1)cosr=a+4; -1 <a+_4<1; -5<a<-3;oe [-5; -3]; le" "" ro =t' Uo o'z 10<1; a2+6a 2) sinr=6a-az-lo; I 16" d' l0 > li

023.

piBeH" f;:ittii::,-f:i!li

iri;iilliitl::;:tl: AITEEPA Mep3rqK A. r. ra

iH.

AKaAeMi.rHri piEeHb

11,<ot

ttii

503

a.z 6a+ 11.>Ot a!-6a+ 11 = 0; D=-8 < 0, seMa€ EopeEiB,4€ R' 6a a2 - g >O; -a2 + 60 - I > 0i a'z- 6a + I <o; (a - 3)'<o; a = 3. tae RI - o=3. BiAnoqiAb:

_1 b) ,=-

srnr;

1) sin 168" cos 126'< 0, ocl{irbxtI sin 168" > 0; cos 126" < 0; 2) te 206".cos ( 223") < 0, ocliinblcs tg 206" > 0; cos (-223") < 0; 3) cos 4 tg 3 > 0, ocliirr,lca cos 4 > 0; tg 3 < 0.

924,

6.)

= 1,5 cos

925.

ll sin?80'-sinl2 360"-60')" "in60'=;,

2) tg 900" = tg (180' 5 + 0') = te 0" = 0;

3t cosl2O0.=cos(360' 3+120") cosrzo' -cmeo"4) ctE ( 585') = -ctg (180' 3 + 45') = -ctg 45'= -1;

llr/tr\n.,6 coslz,T

5) cos6 6r

"t,[

1l^,)=-"i"[r

926. f(x + T) *

l(.r

T) *

cos

-6

-!:

fr'

5;3].o.zo: .Lg:=t t,ctg'x=J; ' sin x J8a 2 dG lv,{Beprii crg.r \ 0i ctsx= .lg-t=-./g=-g. ,l z0 \lz5 5 Bionoeiat: -!. 5 t, , 2) Lg(t=3i n.,r.3l; l-tg'o z cos- d "o.o=r.[ \ir . tg" a

92a.

r"-i] -",'l-;l-+

l(I).

l) 6inx

rr€ III

cueDri: cos

I' smc<u; stnc- lvr- cos-ci !lOi

o: cos.r-- /1

E = -:Jro= -'J'. -.,f1 r0 \l 10= - Y10 s"to B tnoa th: -",",

927.llg--sil]'x+2i

929, 1 ) sinl o . cosi

2)y=cosn-1;

= sin

a(sin'a -

cos'zd

(sin'?cr +

c = sin" c

cos:-qsjn

- ctg'dsina

93O.

= cos' c

ts'osin'zo)ctgcr = sin'?p(1+ tg?d;"rgo

1-lsinfI+nos.rl': 4)--+= sln d cos d - cigd

at r = coslr 2

cos'z

2ts' a.

(1 + 2

sino

cos

-""l,"r"--a-l sin al I

4{]

5o4 ill: ATTEEPA MepsrrK

A. r. ra iH. aKaaeMieHrar pieenr

tiiiltliiill:iilil

2; EaiMeHrre

iitliiiillliii:| uresPA

(-3).

"tgo=ts'zo

ctss=

2 sin'zc[

I cos2d 1.5, 1.5cos2o=

=2,5cos2d 0,5;-1 <cos 2c[< 1;2,5<2,5cos2d<2,5; -B

cos' c sin'

-2sindcoso sin'd 1 cos0. - -

l) 2cos'?c-3sin!d. l-cos2a-;tl-cos2d)

Hai6inblle

c ein

cos'?a) = sin a;

"o"'o "oI19!lll9 cos2 d(l sin'? d) - cos' s cos' c = cos' c;

= sin'

< 2,5cos 2c[

0,5 < 2.

MepsrqK A. r. ra iH. AKaaeMiqHrafi piBeHb ::i::r 5o5

e31. 1)

sin(;

= cosc[

+ cos(n

cosd -ctgCl

"m(o

"i,,tn

o) +

ic(+

^to

- ol.

2) 10sin

-1 s

*"(". l) -<z' - d) = cos d sin c, - sin q cos o = 0;

"-[" T) ctg,(sn o) r-r.i--i;(;."1

ig'(3?r

) "J -

ciue'.J

2)' 1

-1

932. cos(s + ll) = cos ct. cos P - sin o sin 9; coso= .E-"t"""= si" P = .'/i - co"' cr = u4:o,so = o,a; cos(c, + B) = -0,6 0,6 (-0,8) ' (-0'8) = -0,36 - 0'64 = -1' 1) ctrpourvFMo niBv cacrl'IEv roroxRocri: r cogB\

_ sin

sin g(sin P cos ct 1 cos sin ct sin P

sin d)

n[-o'el =

o'o;

;{},

"i"b.J

= sin(cr + p);

fjglgl

!9i-1

zl.r.i-""'"""1"*'l

'r , Jz "i"o - "gd; rs a = re d. .Iroseae'o.

2sinorosp sindcosp-co sinll ^. 't' cos(o - 0) 2sindsinP-ioscrcos0+sinosinp 2sinosinp * + cosdsing sindqosF p); _ = "i"(" 9J = tg(o * cos cr cos B - sin C[ sin P cos(cr + 0) 934.

P) =

(ct

506

"""(" l)

i::::::

sin(a

<p)

11'

< n4+g. na;oi.'rrme

g"a'e"'o

,{?-6.

- cos 2cr + cos 4cl 2sindcos2c,

sin'

3cr

2sin3c{ sin (r

2sin3a(sin3d sins)

2sindcos2d

sin q

cos

cos' 3d

sin 3o cos

3e !4!q

cos3d

cos: 30 =

cos' o =

- sin'zo + 2 sin'zs- 1= cos'z&+ sin'2o 1=0; 2.os 2d + sin 2d --1 I - cos 4a + sin 2d I 1.

B). Aose,qeEo.

r,,/t < vE-"[" ]J..8.

sin 2d - sin' 2d +.nq' 2fr

"-(T

""out"'*" ",,*""""' -'.8'

A,rlrEEPA Mep3ncK A- r. ra iH. aKaAeMiqH,i piBeHb

sin2d+.nq4d

--).',"*,("-';)-,

cos2d +

2cos'2.I

2cos3([

2cosgcr

- 1 2 cos 3cr cos rx =-=cosq 'J" "." cosa sinc) nos2c-cos6c (cosocos2a sin2dsinc').2sin4crsin2ct 7) f t"trrr "*rrl .lr'5r "lt".r""*r.2"t"r""".'i" ros8o sin4d 2sin4ct 2sin4d ,. '' .os 2.r sin 2d.os 3d 2ein2.t.os2 "i*1" sin'z 4.r - 1l cos'4a cos' 4a 2) \ 8) cos 2cr sin 2cr lzn ) l:n \ lg2o. + clg2o. ctcl +za) +tel - zct.] , 2 "nr2" cos2ct + 1+ cos 4C,

1. .4--" --'

c z; 1-.n, "i"l{+I)+2=0, "r"f{.rl=-r; 6 12 -\-znn,n 2 l6 r2,r \6 r2l xr r^_ r= 12 an 12nn,nLZ: x=-3,5r- l2nn, ncZ. 6 12 2

s36. rr

neZ! 1*,,6=o, 2t 2cosl I 1l J:,: I \3 2) "o.[12 3,r 2 2 3 r5trr + +zftn-nF/. x=!a+5fl 2n +4nn.neL. =+ e 263

BiAnogiAb: 3,5n + 12nn,

I ^ 7r llt - o.]) =J2coslct-;l; lr cosa+sind=sinl;:-.t]tsino -zsrn4rosl4

u/t49s;n1.r

5. TprroHoMerp14qHi piBHrHHr i HepiBHocri

2sindcosB -sin{o-p)

tg (0 +

a) < 1; -J149 <

cos 6c[

"o"''"

-"J2cosd' J2sinc{ J2sin<r J2costr @-tL-

9 cos cr1 =

"*2" ^1 2sin2d'os2G cos40.sin4d cos'/40.sin2scos20 'os 4(I aos" 2ct sla" 2 cos4d 2

l*oJ vz-"o-rl-"1""",r "r"|"r'"J

#"'*

- sin

sin !9d + P) = sin lq + 91. Aoeese.o. 2) CDporrvcMo niB) qacrxnv roror{socrr:

'6 "o"o-z"osl

sin(d

sin 6a tg 3& +

tc(1

"""a "tg0) sinasinUl;in" -

=cos: cr(cos'?(1 + sin: o)

r-^l 1 ,l

sjnctsino(ctgd

=2sin3a+2cos'z3cl=2; 4) cos{ cr - sint o - cos 2([ + sin2

l) "*[ie'c 'J -â&#x201A;Źct{l -Lg o) tgcr -1. - tgd.tclg:d(1 tg'd) tg'a {l- tg'o) "tgo 11 ts,ct. I

933.

a=10:b=

2sin30 . 2 sin (1cos 2d = 2 sin 3d; 2sin0cos20

-ctgCI

cr)

(} 2 sin d lr I +sin2q los ts .., cos2fl = 2 cos' cr =

0 tg a ,. =sina ctgte" -'

".""

Tcos

Ja +t" = Jtls: l0sind-7.osrr. | '"-sinc .'- "o.o .,/t+s Jl49 ) \ Jl49

935.

tsn -"ielt

= \,/i4g(sin a.os

o) + ctgtt + crl =

+ ctgcl = 0;

cos(21r+cr)tg(n+(r)

.IJr.neZ "ta ctxfi+nn,nez'

d*!+

2) 4 cos'? Cl - tg d ctg cr - ocEinr'(r rarii sHartelrEs rle icEyloTl'.

:::::::j:::::::i::j:::::;:

Bidnoiidb:

!! 33+ !

+ 4nn. n

ln \l \ 6/

znn.n.z;

eZ.

..:titii::ti:llitla AITEEPA Mep3ncK A. r. ra iH. AKaaeMi,rHrt piBeHh

lr.l

507

3+Gicljr-;J

1t 1l --+fin,n€Li

/n\r

nfi t--=

=oi ts "\ i- 4'l=--;Jg x

l,=!+znn.n,z,

6+fin.nELi

4cosr'

=--+fin,neL,

-ft+ nn, n eZ. 41 4cte @r - 9) - 8 = 0; cte(3r

9\ = 2; 3r --9=arctg2+fin,neZi

x=z+Iurcctez+T,nez 3 +

larcct'e

2 +

n\ r , n -." 'r n''nczr - =(-j) '=1-1yL-!r,nn,na7' ;' ";)=;, = n = t: (-tt' -[+ n = -I-.:" ;. [ /

eaz. sin[x

Bionoeiat:

e38. .osf

r, Tj

-l' I

"rO.

t?! - 2nn. n cz;

- 2"".

e3e.

4tg'x -7

r 2-'2siII't lsjn r = 0r

94O. 1) 2cos?

- 2 =O;2sin't + 3sir '= ]x =nn,ncZt x.fln,ncZi

3sin

hidnosiab:fin.n€2.

".,-

t + 3) = 0;

jr=0;1

2 sin'? x + sin [-1; 1].

l,="

= O; 2 sin'

t -

sin

a 1= 0'

-znn,ntzt

l"i,x -r, l,=rtr,L,

"x.*.2.

ez'

++znn,neZi l-r\*tI+ 3) 2cos2"t Scosx- 2 O,2(2cos'zx I) 3cosx -2=0i i.*'t -Z 3cos jr -2'O; 4cos -r-3cosx 0: cos n(4cos r- 3)=0; Bianoliab

5oB

nk' k

l{!l ATTEEPA MepsniKA' r. ra

Bianoaiah: ':

+'-Y: 42

6) 2

Ixopeuie xeuae'

r = 1, t € 2t,-t-t=O.D=9i i =1: lsin.r=l: l-3 | ' I i."=- t'lU=_U: ; I I I

SaMiEa: sin

2 = 0; 0; sin n(2 sin

iH. AKaaeMi'{Hr4i

piBexr

ll:i{ii;ii:iiii;i

tgx 1; t"*=-1,

n8"t=tt -

t -

lz"in*-a,0r lsin'=' l,s:

2) cos2t+sin

Asin

3tg'zr + 3tgi

8+ l+ Lg' x

1+ tg- r.

=0;

r + 4Lg, x 7 o, SaMiEa: tg" = t, t>O.3t, + 4t:7 = 0; ) = 100; [r. = t, t. 7 tt.z=-4+lo ilr^ 7. -t - Be ra4olonLu'c , 2 0: O 3 t' f_

BiAno^iAb: 2 Kopeai.

t) -

:::::Urlg!,

1_,tl -" 1^= 2" ''

8cos'zr+ 1=0; OA3: x+f,+nn,neZ.

r+Dg-.r

tt . 3rI n=zt ^ x,' = ft*tn-U, 2 2 i-zlt-Ti sjll2

't!:4.il.:l_.

f,+\,nez.

tg',

Slga {-+

= Ssin x + 2i 2(1

arccosl + 2nk, k eZ,

= tg

ate,r-j._+1-o: - 1+ tg'.r

w;= \ ; -;1nn'n-z: x -f,tznn nez:

n=1:rr=

l,*\.t.zt 5) 3

ez.,

Bianoeiat:

2s\t\

Bianoeiad: =.

l, ; ,*.,-.. l, -^u*"!-zn*.x.2.

t + clg x; OfiB; x+!+2nn,nEZi ,+fih,keZ. 2sin2y=llri+!9!J; z"inz, "in'':j9{l ; 2sin2x. 2- ; cos,r srnx .1n2r 2sin^2'-2 2s:tn'?2t-2=o: 11-cos4ir-2 0, l"os4x t: " sin2x x.!!.Lz: lsln2x*0: l2x ' nt,teZ: 2 n 2nm.n-zt l.=I-Y,^,2; lax l)42

- =3{ t !. n"' " -zt 3n fi - -gr-8,I = 1t ,=0,*.---3-u z, =

znn, n eZ; t -+ 2

BiAnMiAb:

Biinoeilt

Bi}noailt:

3 = 0;

t-^tL-"'=;,

arga

'\tnh'k-Z' :

+ fim.

m.7-

hc 7

tgx rScrgJ.=5lO.ll3: x*tr -nn.n-Li 2

fih,

k.Z.

saMiHa:tsx t; crs.r=l; zr+9-s o; 2!' -!i--2=ot [2" sr 'z=ot t t / li-0; - r,rr ,.ffr, ,. lx=alrtst,l-nt,tez; I ltSx=I,b: x n tnm.net. lr'z-ri lLg'=r; L 4 lr+ft Bidnolilb: ar.tg t,S nt,I.Z: I-nm,m.t. 4 7) sin r + 2 cos r = 0: tg t + 2=O; Lg x= 2; x= -erctg 2 +nn, ne Z,

BiAnosiAb: arctq 2 + nn, n e Z.

dl Jsfn x,

iiii:ilii{lilll:

srn x cos ,r = z cos;" xi

r sin-rcosx ,-F-. J

Ssin? cos-

2cos':x

=0;

AITEEPA Mep3rrK A. r. ra iH. AKaaeMi,{Hxi pisexu

Itl

SO9

3lg"+tgt-2=O.

13)

gaMifiai tg n = t. 3t2 + t

z .r"- rlb f,, ?, o Ifr"'- o 4 ' I "

sin,

-USIn''f + bsln I

coa ,r

2; 5sin

cos

ZCOS/ .f,

r sinrr-

3sin'zr

cos'x

lr=r: frs,r= r r'.,= '- u,, a i l, _2.l---_2.

l'=n

lz'=nn'n"' l,' T.,.t' lz,. |. o*.*.2; L,=X.V.u.r.

Y, n eZ; itt, n.z. 14) 2-sin'z:r + sin 3x sin r= l; 2 sinr, + B sinr - 4 sinrJ._ sin r_ -4 sin3r + 2 sin,r + 2 sin r=O;4sin3, 2 sin?.r- 2sin.t + 1=0. SaMiEa:sinr=r,rEt 1;11.4f - 2t, -2t+1=Oi t=rtltlr 4.;-2. _2:+1=0i Bilnoaioa:

2(sine:r + cosr.r) =0: 5 sin.rcos.r 2cos'-r

\rc, x -|tgx-2=o. 3aMiHa: tg x = l. 3t' 5tt2 O;D=ll

+ sin 5r- = 0; 2 sin 3r cos 2r = 0;

Lcos2r=o;

-fr + nh, h eZ.

lsin3x=0.

l'-a'ctez-nn',-ez'

1,,=-t; ltgx=-r; la=-\anp,t?.7. '14

Bilnoaida: arcLe?-nn,ncZ:

9\ 2,5sr'l

sin

2 = 0t D = 25i

-+-=O:

0=0:

at' zt" zt+rlt-)

+nn.nez:

4t _ 2r2

f/,=;; lrcr=i, l,=**"?"-^o.u.r.

! + nn, n e Z: arclp? r nk. h cZ. "3 4 2x ^ x cos srn' ,x - cos'lul'222222 cos- - l.Dsrnr=l: -Jsrn - - cos' -

-- il+l

i:':{.!-::.i:i

14(

-2t +1

Bidnoeida:

.in"!+s'i"ico'X=o: sinfl2\*nj+3.".{l=0, z=2fin,nEZi

tc|=

Itel*a=0,

l,i.I2 = o,

| 2' 'l"i,r-r-"|-o;

L =ftn,neLi

= (r:

[x=2nn,neZ:,

lf,= -

-z

arctc} +

nh. k

ez;

lx=znn,neZt

2l=0;

lx=-2arcts3!2flk,he7. iilnoaila: 2nn, n e Z; -2 arctgg

+ 2nk, k e

^ lsrnr=u, lt"."r-t=0, 'lst5

r = 0; 10 sin r cos r - 2 sin r = 0; 2 sin r(5 cos r fx=rn,neZ, lx= nn,nez, I t I + 2nk- h e z. 1"o", = , Ir = t

Bi6ni'oai0o: nn, n

e Z; larccos! +

11)

5 sin

12') si^2t

2 sin

-1) - 0;

"r""o"

"." t-"''

2xk, h

stnzx.

eZ,

( ,z "x'\( ,x +s'n',.r) 2Jt lcos---s'n-rJlcor2 cosr=0; cosr(2sinr- 1)=0;

=cos; l;2sinrcosr f0, lr =a+ rll, rez, lcos.r= o, l"i.'= ]; I x r_tf ! + na. eez,.

Bidnoeilo:

510

! 2

+ nn, n

-l

ezt (-tl'E+ftk,hez.

i::i: AIrEEPA Mep3rex A. f. ra iH. AxaAeMi,{Hran piaenr i::,i!!:i:ii:ii:i.;:11

Bdnoaidt:

!.n=Zi z4

l.t)"

! . trk.kcz.

t7) sin'z.r.cos?2,!+sin'3r--3: l-cos2r '' l+cos4_t. I cos6r 2' 2 2 ' 3 cos 2.:!+ cos 4r - cos 6r= 3; cos 2, + cos 6, - cos4r= -nO; :iiilit:li:jllt;

AITEEPA Mep3rex a. r. ra iH. AKaaeMi{Hrai pise6r

i. i.:::i 5r r

2 cos 4-r cos

2r -

cos 4x = o: cos 4x(2 cos

=!-on.o, 2, l,

*"2,

Bidnosidb

18)

cos'1

=;-7.",,.

lr,=,i-rou.o,r,

:- :-, 846

,r +

2x-1)=ot [:""n1=o: ' 2aB2a 1= 0;

cos'z

l, =X,T.^.^

), -;, ^o.u,r.

Bino'idb:

8xi

t- cos?

l+cos2r l+cos8r l.cos4-r Ircos6t = 2 , 2 -2 ' 2+ cos2t+ co68r= 2 + cos 4r + cos 6r; 2 cos 5r cos 3r = 2 cos 5.! cos 5t(cos 3t - cos t) = 0; 2 cos 5r sin 2r sin r = 0i .lnnn l r lr=-+--nc7lcossr 0- Itx=-!ILn,ncL, | 10 5 ll'lahlsin2r=0. l2x=nk.hez. , i.,u.r. I sinx = O: lr=nm-mez: lr=\m,mcZ. 4=xm; *=2m. aianoaiaa:

941.

nezt

lfi+!,

+ cos

> 0; 2fin < x < ft +

sin a = 2 sin

+ cos

tg"r+ I -0:tg-r

zrn, n e Z:

r; sin r ti

+ cos

Ylrr5]I-;' 2nn' n ezi ,\ .or;< ;'';. ^,. ;' 2! r 4nn, n .7. n 4nn . , .!! 3U t ,n 101! ) annt; + 4rn l. n ' 7' Bid\osidb: l';' s)

"i"(,-i) !

| ff

2,1n, n

e7'i

{t+

rcl;F;ls:t, z,nn'i '3'6 ,t! * "".a < !+nn,nez; 63tt 22+ snn

: x=4+nh.kcz. 4

-sinr=2sinr+cosri Ssinr+cosr=0; 3 tgr+ 1=0; l1 r=-arctg-+nn-ne/. tsr

-n 1

SaaoBorLsr. sin x. 0; .t = - arctg : + ,rs, s BiAno6iAb: Eane)xaft IOi 2nl,

sfi

<x <

""" -'

+ 3nn, n e z.

-1 |\ZL)"i' + 3nn: ')+}nn],ncz'

?-'-ll >-t: nn.4 !:3!,nn.n,z, L * nn .?! 3!r i! a nn, n a7i

o, *"1

--:

512 lll: AITEEPA

+; -! * z^,s,,i=!+

Bidnolidh:

t - L + 2tn' n ez; "", " I -ff+znn<x<$+znn,nez. , znn; znn)' , . z' nianoeia,.: -

-2!

ln 2ftn + 2nn\ n e z. l'r+ ;t ^; 7- l.

= 0;

t=-!+nn.nez. 4 3anoBo,r6gse sin x >

2fin

"'!

]nr.rezr r =larccost*2nh,heZ. 55 Bilnoailt : ! arccos4 + zfik. h e z.

1) cos

-2nn,ne7t + '' 3630=znn<zx='lr-) * znn < 2x <1! + 2nn, n ez; -L26 n3n -;+r,n<x<lr+fln.neL! + n4 n ez Bidno'iab: #+ nn ). \ x [ fr -nn.n-lt 'h t

e Zi

942. sin rl= 2 sin

+ zxn, n ez;

+,kez.

Lg(5 cos .r) = 0t 5 cos x = fin, n

"o""

2nn

12 3

FZt !' | fth. k cZ.

4,r = cos? 2-r

.tt

ltsin3x> 2 i \ t znn <3x <8 44

943.

zfi

"*te|

554a t +nn<-<-+fin,nâ&#x201A;ŹL' 2x 19n 5521) 19r , fi+'fin<2xt-+'fln.nELi

I - arcLg;

Mep3rer< A. r. ra iH. AKaaeMi,{Hxi piaerb

l{::iittalij:iii

r::::iitili::iiti: MTEEPA Mep3rcK A' r' ra l7Ycl ln l0M,!

iH' AKaAeMi'{Hxr piBeHb

i!:i

513

n .\nn 2282

19n n

Brtnardt,

5xn

:JnD 19n :inn i .n

I I n I' ,o. .,r,cos'3 2Iar.s,' /3 2 "n"t o , 23 : f,t -,"'t-r, 2r sit.,r.sir', ".".n"' "i,,r 3:63:

944.

'r4I ./li. tl .c zi,

3r rs' 2,r

...,,

1).a l 3j'r'."s

6ill

: ,r ctCit in ;,r 'i" 3 - 0 6 "tC " "tA r s,1l=0. : 21 945. l)a=nrcsilr(.r 5); t!x 5:li4<i<6; 1)(a): [4;6]: 2) u = arccos (n! 15); 1 ! xr 15 < 1; ]r'

l''

15.1, ljr' !

- r; :

-rr

'"'

16,

t+;

,tqr: [-r; -,]rJl!,1"r.r; a ; 3) V .arr,tgu/y1 2i r + 2 >0: r> 2i D(ul. | 2; t*).

q 2ar(sin:r- 1, -X:"*"r"r'.ii -n:2arcsinj.!r; t5n3n n 3n 5nr2,rc,r!r. I l:l.ttl

946. 1)

141"44

2) , . 5 3 rrcctg 2.r; i) . urcctg l}- r; 37r ' 5 3ir . 5 3 arrctg 2 ' 5i t(y): (1, 3ri 5).

q47 lr.rr,.",r=

ll: Yl!

;l arcctg 2.r ': 0i

/,,

Rr,ln,ntnt,: Y

5n. tt,r",,it

::r ar,r:r, ;Jl

arccnsl

Bidnoair)r:

1) .

2n i

:lt : l

]. 2

.r1 arctg(:r

+.1:)-

ltan'nutr: ! \I

4*!, = |: :. r J; = *, . = '

'11

.i 1.1