12390 - Математика. Справочное пос. Для школьников ст. классов и пост. в вузы by yahya rafiyev

А. А. Рывкин, А. З. Рывкин

Математика СПРАВОЧНОЕ ПОСОБИЕ ДЛЯ ШКОЛЬНИКОВ СТАРШИХ КЛАССОВ И ПОСТУПАЮЩИХ В ВУЗЫ

Москва «ОНИКС 21 век» «Мир и Образование» 2003

УДК 51(075.3) ББК 22.1я2 Р93

Р93

Рывкин А. А. Математика. Справочное пособие. Для школьников ст. классов и поступающих в вузы / А. А. Рывкин, А. З. Рывкин. — М.: ООО «Издательский дом «ОНИКС 21 век»: ООО «Издательство «Мир и Образование», 2003. — 560 с.: ил. ISBN 5-329-00906-5 (ООО «Издательский дом «ОНИКС 21 век») ISBN 5-94666-123-Х (ООО «Издательство «Мир и Образование»)

Справочник А. А. Рывкина и А. З. Рывкина, выдержавший четыре издания, хорошо известен учащимся и преподавателям средних специальных учебных заведений. В настоящее издание включен материал, предусмотренный школьной программой по математике. Книга содержит: основные сведения по элементарной математике и примеры решения типовых задач; элементы высшей математики; краткое руководство по простейшему анализу исходных статистических данных; сведения о практике приближенных вычислений и шестизначные математические таблицы. Пособие адресовано учащимся средних школ, колледжей и абитуриентам. УДК 51(075.3) ББК 22.1я2 ISBN 5-329-00906-5 (ООО «Издательский дом «ОНИКС 21 век») ISBN 5-94666-123-Х (ООО «Издательство «Мир и Образование») © Рывкин А. А., Рывкин А. З., 2003 © ООО «Издательский дом «ОНИКС 21 век». Оформление переплета, 2003

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9 # # = 1 4 9 999M7 = @ 9 1 @ = ; 1 < @ @ =: ::M: = 1 @ =D 1 4 := ==G: = ( @ 8 1 @ 9G 1 4 7=8 8D = @ CEE ( @ =CEE 1 4 =EDD G @ = EDDG ' # # U M 1 @ 9E 1 E E=g 8 ( @ M 1 @ D 9 1 E E=9g 8 @ 8 7 1 E E=g

7 @ @

% # % = * @ 7 C9 = 2 @ =7 * @ 8E 9G B % # % = @ E = * @ E 7C9 = @ E E= * @ E = @ E 7C9 U + # . 1 & ( M 1 9E * * ( " M 9EE ; #6 / &<

9 # # = 1 @ =M :C:8 7 = 1 @ 7CD 1 @ CEC: G: 7 @ E CEC:G: 7 = ( @ M 1 @ 9 CC7= 7 = @ 7CEEEE ( @ = =8G 7 ' # # " G= 1 @ =DEE 7 1 E E7g M ( @ 9E MD 7 1 E E77g M @ =E 79 7 1 E EMg = ; / 0 GE : 8E ( 0 DE : 9E ( @ 79EE ( @ =EM7C 9 7 @ @ = EM7C9 = . ; 1 < ; GE : 9E ( < @ 87EE ( @ =9CD: 7 7 @ = 9CD:7 = . ; DE : DE ( < @ 8DEE ( @ =D8GG = 7 @ = D8GG= = @ ;=EE : =EE ( < @ 9CC77 C 7 @ @ 9 CC77C

- /

= 1 4 G: G=M: 8 = 1 @ =D8 ;9EMD< 1 4 E 8CM:= 8 = ( @ 7: 1 4 M :=7= 8 = * 4 =D 8G:= 8 = 2 @ =78 ;@ =:7G< * 4 7G 8=: 8 @ @ E E7G8=: 8 = @ E EE= * 4 E E=D8G:= 8 @ @ =D 8G:= 8 = @ j 8E 2 @ 8E : 9EM D 8 @ @ =7 7GG = @ = 77GG = ( @ -----=E = 1 2 @ = --- @ = C8DE G = @ 9E @ 9M= C7 = @ =E @ =77 GG

9 = @ 99 9999 # ? M @ 9EE = @ MD 4 9 7DDD: = @ 8 @ =7 G = 2 @ 87 @ MD @ 9EM D ; < = @ 9E 2 @ =D 8G9

7 @

9 = * ;bd A bdez< @ 7 C9 = = ;imbdr< @ ------ * @ E 8C7::G :7 = = ;sbdx< @ ------ * @ D @ 7 ==DD: =7 = 2 ; r A mmr< @ =7 * @ 8E 9G = ; o A pqo< @ 8 2 @ 8D * @ M= 99 = 2 ; A przmn< ( @ D 2 @ :7 * @ @ = G7GG = ;qo A qmo< @ =D C 2 @ C C @ C E7M7 = 2 ; q A qsmdc< @ 77E @ DDE 2 @ @ 7E= =DG = ;ep sx a sxdcrz< @ ;Pu< @ =EE 2 @ @ DEE 2 @ =G7 GG = ;ep sx a sxdcrz< @ ; < @ =7E 2 @ @:7E 2 @ 7=M 9CD = ;ns spdo arpr rx nbsx< @ @ G 2 @ =:DE @ C7GE 2 @ =DEM 899 = ;T [ A Tdrxqdprbmdps p rbeps [bsx< @ @ =E . @ DEEE 2 @ =G7G G @ = G7GG = ;spdo arpr rx sxpc x< @ 8 @ =C G9E 2 @ 9G7G E87 @ 9 G7GE87 = ;dp rbeps axp sxpc x< @ 8 @ @ =G EEE 2 @ C 9GD9

9 = * ;bd7 A a pqx bdez< @ D 9C=D 7 = 2 ; r7< @ =99 * @ M7M E8E9 7 4 E EM7ME8 7

= ; o7< @ M 2 @ =7MD * 4 E G8D=7: 7 = 2 ; 7< @ 9 4 8 899C= 7 = ;qo7< @ 8E 7C 4 7C 7M7M 7 = ;qmmo< @ 9E 4 =E== := 7 @ E =E==:= = ;p A peqx< @ 9 4 E 9E9DGD = ;ns7< @ D9E @ @ 7CG MMM @ 7 CGMMM 7 = 1 ;rm dazbi < @ 8D @ M8 78MD 7

;

= * ;bd8< @ =D 8G:= 8 @ E E7G8=DG 8 = ; o8< @ 7: 2 @ E :D9CCC 8 = ;arpe < @ =EG 2 @ 9 @ @ 8 ECG77 8 = ;smpo< @ 9E 2 ; < @ @ = =87D: 8 = ;smpo< @ CE 2 ; < @ @ = 9=CG9 8 = ;emqo< @ =7D 2 ; < @ 8 CD:M7 8 = ;emqo< 1 @ =7G 2 ; < @ @ 8 D79CD 8 = ;arpdopqo< @ =DC 2 ; < @ 9 D:78 8 = 2 ; 8< @ 7=D 2 ; < @ @ D ==D99 8 = 2 . ; qp czr rmd< @ @ 9E 2 @ = =87D: 8 ; = < = ;qxcbarxq rmd< @ =EE 2 @ @ 7 G8=DG 8 = ;qmo< @ =E . @ =EEE 2 @ @ 7G 8=DG 8

9 = ;cqpbd< 4 E ED9:MGM= = . ;oq A oqpezn oqpn< @ 7: 898:C 4 = ::=G9C = / ;m A m dex< @ =D . @ 98: C 4 7G 89MC7 = 2 ;s A im do< @ =D / @ =D7 ;@ 7CD< . @ @ :EEE 4 9C8 CM79 = ;armdx< @ =9 2 @ D 8CE7M8

= ;azmqr pqrxq< @ 7C 2 @ @ == 88MG= = ;cqmaa pqrxq< @ 7G 2 @ @ =7 :EECM = / ;exdrps< @ =EE 2 @ 9C 8CM79 = . ;e r A z doqxo xbczr dxr azmqr< @ = / @ =EE 2 @ 9C 8CM79 = . 1 ;e r A z doqxo xbczr cqmaa smdc< @ = ; bdrps< @ ==7 2 @ @ CE GE78 = ; bdrps< @ =EE 2 @ = . = ;az rd A azmqr dxr rmd< @ 7EEE 2 4 E ME:=GC = ;rd A cqmaa smdc rmd< @ 779E 2 4 4 = E=DE9: = @ = =7 . = @ E GM7GC: .

7 = ;cqpbd< @ E ED9:MGM= = ;aeq isx< @ 7E @ = 7MCMG = . ;oq A oqpn< @ 8 @ 8 GG:M8 = / ;m A m dex< @ G . @ 9GE 4 8= =E89G = 2 ;s A im do< @ =7 / @ C:DE @ 8:8 79=:

4 @

1 = ;cqpbd< . E ED9:MGM= @ D9 :MGM= = ; A epqpr< @ 8 EGD @ E 7 = ;o r A ixdd xbczr< @ 8 GG:M89D = . ;oq A oqpn< @ DE @ 8 GG:M8G = / ;m A m dex< @ G . @ 9GE @ 8= =E89G = 2 ;s A im do< @ =7 / @ C:DE @ 8:8 79=: = ;nbrx< @ =f7E @ E EE879EE @ 8 79EE = = = ;ombr< @ ------ @ ---------- @ E =8C 79 9GE = @ = @ = = ;ixqbmr< @ --------------------------9GE MDEE 7E @ E EED:C = @ E EEE7G= = , ; spd < @ -----79

@ @

9 7 @

= . ( ; s oq A s bo oqpezn< @ 8 CC=G:C 8 = ;nbdbn< @ =fDE ( . 4 4 E ECM=M:M 8 = ( ;rxp aimmd< @ 9f8 ( . . @ @ 9 :8CG8 8 = ( ;rp sx aimmd< @ 8 . ( @ @ 9 ( . . 4 =9 7E:C 8 = ( / ; s m A s bo m dex< @ G ( . . @ 7G 9=C 8 = * ; bdxcspaa< @ =D ( . . @ 7 ( . / @ CD G8E 8 = ( ;cbss< @ C ( . / @ E =97E:C 8 @ @ =97 E:C 8 = ;ir A ibdr< @ 9 ( @ 7E ( . / @ @ E CDG8E 8 = ; r A pqr< @ 7 @ 9E ( . / @ @ = =8DD 8 = ;cps A cpssmd Tnixqbps< @ G @ =DE ( . / @ 9 C9D9 8 = 2 @ 89 M: @ =CG MG 8 = 2 @ 8D @ =D8 D:E9 8 = . ., ;zzo A zmcazxpo< @ C7 7 @ 78: 877EG 8 = ; rr< @ =EC @ 9:: 8:7 8

= ( / @ = E9= ( / @ @ 7M CGEE7 8 = ( @ 9 ( . / @ ==G 87E= 8 = @ 9 ( @ E 9:87GE 8 = @ 7 @ 87 ( . / @ E M9DCDE 8 = @ 9 @ =7G ( . / @ 8 :GD79 8 = 2 @ =CG MG 8 = 2 @ 8= C @ @ ==M 7D: 8

1 a % -&b/ = @ -&c/ & @ 87& ? = G &Z E& ; < @ A=: ::G& ;Z< &b A9E A79 A8E A69 A7E A 9 A=E A9 &c A9E A7 A77 A 7 A9

=E 9 7E 69 8E 79 9E

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1 8D7 0 . 8=M * . - 8=M * ( :D / 7=M =9D 0 / =98 * . . =9E 0 =9E DM 0 778 0 2 / 7CD 7C: :: 0 0 GC 0 9C . . 88E 2 / 7C8 797 C7 2 =7: 2 9: CD CG

( =:M \ DC

\ 798 \ 8D \ 1 7DC 0 0 1 1 7DD 0 1 7DD 0 0 7D: \ 7DC 0 0 1 1 7DC 0 7DD 0 0 7D: 0 *- =7M \ GG \ > * =8: \ =CD 0 1 =CD =C: 0 7=D 0 =C8 =:= \ 1 , =GG 0 , =GM 0 , =GM \ =MC 0 2 =MC \ ( :C \ =9E

. DD

+ 79D + / =E7 + =E7 + 797 + :9 + - / 2 8DC + =C8 + . 8ED + 1 =G7 0 =C= 0 78M 0 =C= + 1 78D 0 =C9 0 , 788 + - 9C + 2 / 7D= + 7C7 + ( 79: + M= 0 0 G: + ( =C: + 1 =C= 0 0 =C= + =CE + =C= 0 0 =C= + 7G= + C9 0 0 0 . D 0 0 0 ( . 8DM

+ GM + *- =7D 0 2 / 7D7 + D: + 9= 0 =D + ( =CD + ( =DG 0 . =D8 + 88D + 7:C + ( DD 0 0 CG + 7G= + =G7 0 =C= + ( *- D + =9= + ( =D: =DM 0 =CC 7=D + 8= 0 D7 0 . C

/ 89 Q * . MG Q , =GD Q =79 Q =7G 0 0 *=7M

Q =:: Q 2 2 / 7GC 0 0 7:8 Q . C= Q 2 =CG Q 78C 797 Q 79C Q =MC 0 =MC Q / 799 Q 1 7DD Q C8 Q =:: Q . D9 Q =C7 Q =G7 Q 2 2 / 7C8 Q 2 2 / 7C9 Q 2 . 89: Q* 8==

(

* 8=8 3 . 8=M 3 8M 0 == 3 / ( =9E 3 =G7 3 D=

3 ME 3 78C 0 9M 3 9C 3 CD 3 8= 0 0 / 7G 9D 0 0 ( 8D: 0 CD 3 799 3 7=G 3 8= 0 D8 0 1 77E 0 0 =:= 0 . 9D 0 0 ( . C= 0 0 . C= C9 0 0 . D 0 0 ( . 8DM 3 78 3 78 3 2 / 9=G 0 89 0 2 =88 3 =D9 0 . =DE 3 89: 3 ( =D: 3 j* / =9= 3 R 797

3 78D 0 79= 0 78M 0 , 788 3 9D 0 / ( =9E 3 22 / 7GD 0 7GG 0 ( 7GG 0 4 7GM 0 7GD 0 2 / 7GC 3 22 / 8=8 0 0 8=8 3 22 / 2 7:: 0 2 / 7:8 3 22 / 2 7:C 3 79D 0 ( =DM 0 0 79E 0 0 8=E 0 8== 0 . ( =DM 3 , =GD 0 1 =GG 0 0 =GM 0 =GG 3 ( =8M 3 =C8 3 =9: 3 2 / 7C: 7:7 3 :G

3 DM 0 9E 0 8M 0 89 0 0 8D 7M 0 0 8D 0 0 1 8: 0 0 8: 0 7M 0 1 / 9E

=9D 0 >!3 7C 6 / 79 9D

7C8 ' 79: ' 7M7 8EG ' 797 0 79D 0 7DM ' =C= ' =G: ' 2 / =MG 0 7G 9D ' 8=M ' 7M ' - / 2 8D8 ' . 2 / =MG0=MM ' =:7

C9 0 0 0 C 0 0 0 ( . 8:E 4 =C7

4 ( . 2 89: 4 , =G: 0 1 =GM 4 2 2 2 / 7G: 4 =:M 4 88G 4 / =98 4 / 8=7 4 7M= 0 22 / 8=8 0 7M= 0 7GM 0 8EC 0 7MD 0 0 / 2 / 7MM 0 0 / 2 / 7MG 0 0 / 2 / 8E8 0 0 2 / 8E= 4 2 / 7GM 0 8EC 4 7ME 0 7M7 8EG 0 7M9 8EM 4 7C9 0 . 87= 4 ==D 4 / 8:8 0 8:8 4 / ==M

/ :G M7 0 99 9C 4 * / CM 0 . MG 4 =9= 0 :9

78M 0 0 , 787 ) 799 79C ) ( =:8 0 0 7:8 0 0 ( =D: =:8 ) =M: 7=M ) =D7 =DC 0 D7 0 D7 ) ==G 0 :G GD ) 2 / :: 0 2 / 7CD ) . G 0 * 4 7: ) =G9 ) 79: ) / =D: ) =89 ) 9D 0 j ( =9E 0 ( =9E ) 9M ) ( C= ) / 79D ) 87E

) 79= ) ( / C7D ) =M= ) . > 798 ) / ( =D: ) / =CE ) j* / =9= ) 79G 0 - 778 0 / 8=7 ) 2 9: CD CG 0 CD 0 DC ) / ,22 / 8C9 ) =M: 7CM ) =MD0=M: 7CM 0 ( 7CE ) 7=9 ) 7=: ) =MD0=M: 7CE ) 1 =79 0 0 - =79 0 . =78 ) ,22 / / 8C9 ) ,22 / 8CG 0 879 0 ( =8G ) / 87 ) DC ) 7G8 ) / 7G9

) / 8ED ) 78E 79= ) =D: 0 7G9 ) =GD 0 D8 0 D7 ) 797 ) :G

6 /

. 8=M ` \ 798 ` / 8:8 0 7:9 ` 22 / 8=D 0 ==D 0 :G GD ` 778 ` 2 =7M 0 =88 0 =8E =8= ` 2 =89 0 . =89 ` 2 =87 0 ( . 8:E ` 2 7:: 0 79C 0 2 / 7C: 7CG 7:7 ` 2 22 / 7:: 0 =7E 0 MD ` 2 7DM ` ( =9= 0 :9

` =C= ` =CE

877 H 2 / 7:M H , =GG H 2 7=C H 2 =89 H . 2 / 8G7 H / =98 H / =E7 =E8 H 7:9 H 8CE 0 =CC 7=C H Q * . MG 0 ==D 0 . ,22 / D: := H 2 / 7:M H =79 H =C7 H 78C 0 9M H =G7 H =G: 0 =ME 0 =ME H =G7 0 0 =ME H =C= =D9 0 =D9 H D= 7C: H ,22 / DC

H ( =8M 0 / . 97 0 1 :D :: 0 =8M 0 / . 7G H 8CE H 79D 79G H . 2 =8= 0 9: 0 9: 0 9: 0 7G 9D 0 0 9D 0 0 C7 H / 8=7 0 8=7 H 2 / 7D7 H 2 C9 =99

8 1 -

;>!3< 7C 0 0 0 6 7C > 1 - ;>!)< 7D > 1 - ;>!'< 8E > ( - 1 =C9 > 79D > 2 7DM 0 C > . ( 7D > 79D 0 7=G > :9 > *- =7: 0 2 / 7D7

> 7C8 > :D > . =9: > . . 8=G > 2 / 7D8 > 7GM > . ,22 / D: := > 2 7DM > / 89 0 / 89 > 22 / 2 / 7:9 0 2 / 7:= > ==9 0 Q =79 0 / ==M 0 ) 1 =79 0 0 - =79 0 2 =7E 0 H =79 0 =7C =CC > 7M > *- =7: 0 2 / 7D7 > 2 / 7D7 > 78 > 2 / 7CD 7:G > ( 8ED > . 798 > 7:8 > 9D > 79D

> ( =8M > * =8: =GC ! . :C 0 2 / 7C8 0 2 / 7C8 0 - :C 0 . 2 / 87= ! =9G 0 2 / 7:G ! 9D ! 2 / 7EC 7C: 7:7 ! - 2 / 7:: ! - 7D 0 0 1 ;>!)< 7D 0 1 22 / 8=9 0 77C ! - 79 0 0 1 ;>!3< 7C 0 =7D 0 0 8=D ! j ( =8M ! j 8CD ! j *- 8CD ! 7G ! =7: 0 0 . =7: 0 0 =7: 0 2 / 7D8 ! 7C7

! 22 / 8=C ! 1 =C9 ! D= ! 7CD ! * 8DC 0 8DC 0 . 8DC ! ( 79D ! ( =D: 78E 0 =CD 0 =CG ! , =GD ! ( =CG ! ( =DG 0 . =D8 ! 8EC ! =E7 =E9 ! 7=M ! / =G= 0 0 0 0 =G= 0 0 0 0 2 =G= ! 7CE ! / =CG ! 2 =7M ! M= 0 0 2 79 ! 1 =MG ! . - 8=: ! =CC ! =C8

! / 7=G 0 78C 0 7=G 0 78M 0 98 0 , 1 788 ! =CE ! 1 8D7 ! =CE 7CC ! / =97 ! / 8C8 ! / / 98 !/ * 8D= !1 8D=

78M 797 798 0 797 0 797 - =M9 =G8 =D7 =GE 0 0 =C9 =:: 0 0 77E 7CD =8: 2 / 7GM 8ED 9D ( =8M =89 0 =8C 0 =8C

=C9 0 , 789 8D 0 2 / 7D7 8D . 2 / 7E= / =:7 0 =:E 7CE =G8 =CE - / =DM 0 / =:E 0 / 8EM 0 =DM 0 4, =D9 0 . - 8=E 0 =:E 0 =DM 0 =CG 7=D 0 . =DE 0 , 789 77= 1 8D= 0 * 8D7 ( =8M =:: 0 =:G D= 2 / 7GM ( 7GM 8ED

/ G 2 / 7C: 7:7 MC 7C: =C7 =C8 ( 8C8 797 78C 0 , 787 ( 7CC =C9 =CE / =M7 777 777 778 0 D 0 22 / 8=8 0 7DD 0 0 22 / 7G: 0 8D9 =7C *- =7C =7: =GE 0 0 79E 0 . =:90=:C 0 78G 0 =:80=:9

, 789 / =87 1 =M9 22 / 7:C ( =E =G9 =DD 0 =DD 0 =GC 0 =D9 0 =DC 0 =DC 0 1 =DD 7DG 0 7D: 0 7DG 0 7DG 0 2 / 7D: 0 7DG 8ED - =7C 2 7D807D9 0 . 77= 0 ==9 0 D8 G7 G8 0 1 *- GE 0 - * G= ( 8D7 0 0 8D7

( 8D= ( 22 / 7GG . D= G: =G8 2 7G7 0 8=G 0 - 7G7 0 0 , 7:M 0 . 3 8=M 0 0 ` / 8=M 7 8 == 78 0 =G= 0 =G= 0 =:G ( :D / / =98 - 7:E 0 2 / 7:E 88G 2 =7: 0 =7G / 79G 0 79G 79M 0 D8 0 D7 0 . 2 / 7E9

7:C 0 7:C 0 2 / 7:G 0 2 / 7:G 0 7:C 0 ( 2 / 7:D 7:: 0 2 / 7:7 0 ; < 7:C 4, 7:G 0 / 88 ( 7CC 8G / 87 / =DM 7G 0 =C= 79 0 0 7GE8 / C7G ( =CE ( 9D / 8G / 1 8G / ( 8M =CE 779 0 ( =9M 0 =:E 0 / 779 77D 0 . - 779 77D =M7 0 0 / =M= 0 =C8 =D7 =CC =CM 7=D

=C9 =D8 =G: ( =8M 6 =9D

8== D: :9 =CM 0 =CM / =D= =97 :G ==C =DE =DC 78: =C7 7=C 0 7=C 0 =:M 0 7G9 0 ( =D: 0 7=C 0 777 0 . 87= * 4 7: =C8

( 1 := 0 ( DC 0 ( 7== 0 2 / S 879 0 0 877 0 ( 79 0 DD - =8C 0 =8C 0 =8D 2 =7G 0 79G 0 D8 0 D8 0 . . 2 / 7=E 0 . 2 / 7E907EC 0 . D8 2 / 7:7 . G 9D . 8C7 ( 7=G 1 7M / 2 / 7C: / :G M7 / 7G 0 7G 0 97 =G7 8CC 1 22 / 8=8 0 7=9 0 :D

1 ==9 0 :D . . 79D =D7 88D 0 8=M 0 *- 8=M 0 H 877 0 879 0 2 / 87E 0 S 879 0 8=D 0 0 . - 8=: 0 0 . - 8=: 87E

=G: 79: 2 =8E 0 0 . =88 0 ( =9E 0 ==9 0 8E: 0 2 =7G 0 0 =7G 0 / 88 0 =C9 79: ( =D: 0 1 =M9 0 - *- =:7 =M: 7CG ( =D: 0 1 =M9 =C7 - ( =D: . . 7ME

7:9 DG ==7 0 ==8 =:: 0 / =:: =MD0=M: 7CG 7=9 / 9D9 7=G 0 0 7=G 0 0 7=G 0 0 777 ! "# $% $ 0 ==C 0 M 0 0 M =D 0 0 M == 0 0 / G 0 0 0 M 0 0 M =C 0 0 1 / M =G 0 :D 0 ( - =EG 0 ==8 79: 79M D - 79: . / 7:9 - *- =GE :M =9D

( 8= 0 D7 0 ( =8M 0 ( . 8D: 0 . 9D 0 0 . CE C7 0 0 . 8= ( 2 DE GM ( / 8M 0 0 / 8:D ( =C= 0 =C8 1 7M ==C 0 :: - 7M =CE =C9 ( , . ( 7C= ( 78: 79 =8D 0 =8D 0 =8D 9D . 79C 0 79C 0 2 79C . ( , 789 0 . , 789 2 / 7C8 0 7ME 8E 2 =77

1 =78 0 =78 0 =77 0 =78 897 =77 0 / 87 / =:= 8CE ! "## 0 7G8 0 / =D= 8C7 8=7 87= D7 0 CC 0 / :G =C9 0 =C= ( =D: =DM 2 799 79: 79G 0 D8 0 . . 2 / 7=E 0 8=: 0 . 2 / 7E907EC 0 . D8 . Q D9 . 8=D

. 7MG0 8EC 0 . 7M=07M7

N / ( H 877 0 ( == 0 ( == N / 8:7 N 2 / 7C9 N =MD0=M: 7CG N 7=C N / 9GD N 88G 0 88G N =9D 0 \ DC 0 + M= 0 0 G: 0 Q* 8== 0 ) 1 . =78 0 =9G 0 M= 0 0 2 79 0 ( =9M 0 0 =9M 0 =D8 0 7=9 0 7=C N ( . 2 / 7E7 N 7:9 N , =GC N ( :C 0 * * :D 0 ( *- G9 N =CE 0 2 / 7:7

N 8D= N 8D7 0 * 8D8 N / 2 / 7C: N / :: MC 0 9C N / =D= 0 8ED N =C9 0 =8: N =7C =CC N 7=: 0 7=D 0 =:G N . D= N . M= N 2 C7 N 7== 0 2 / 7C: 7:7 0 0 . 7E707E8 0 0 7E8 0 0 7E7 N 878 N =C N =C8 N =CC

2 *-

=7D 0 2 / 7D7 _ - 7:9

_ ,22 / 779 _ ( =DG _ =C= 0 =G7 0 ( ( =DG 0 0 0 77G 0 0 0 . ( =DG 0 0 - ( =DG 0 0 - ( =DG 0 0 - *- =G= 0 0 . ( =DG 0 =G7 0 =C= 0 777 0 =:E _ ( 79M 0 8= 0 D7 0 ( =8M 0 ( . 8D: 0 . 9D 0 0 . CE C9 0 0 . C _ ( =8M _ :D _ 78D 0 GG 0 78C 0 ME 0 22 / 8=8 0 / :G M7

78: 0 0 0 7:8 0 0 0 79E 0 0 0 , 788 0 778 0 2 MD 0 4 M= 0 7:8 0 ( 78E 0 MC 0 . 77D 0 0 - 77C 0 0 ,22 / 779 0 0 . - 77C 0 0 0 0 77C 0 / :G M7 0 8CC 0 :G 0 *- 8=C 0 / :: MC 0 . M= 0 GM 0 , 787 _ :G 0 9: 0 9M 0 7== _ =G9 0 =G8 _ - =M9 0 =M7 0 / =M= _ . =9:

_ . 77G 0 . 77G 0 D: 0 ( 2 / S 87: _ . 2 / 7=7 _ . - 8=M

0 =8C

S - =M9 S 78M S 78C 0 0 , 788 S 78C 0 0 , 788 S 78M S 79= 0 78M S 78C 0 , 788 S Q =CG 0 H 7=C 0 H C9 =99 0 > * ; < =8: 0 - ( =8G 0 ( DE GM 0 ( . / 8M S 2 2 / 7G: 0 22 / 7:C 7:D

S . 7=C 0 7ME 0 7M= 0 ( . 8:= 0 7E= S / 7D= 0 7D7 0 7C: S / 7C9 S / 87E S / 7C8 0 7CD 0 / 7C: 7:7 0 2 7C: 7:7 0 7:= 0 7D7 0 7D7 0 7CD 0 7D7 0 7C: 7CG 7:7 0 / 7C: 0 7C: 7:7 0 / 7C: 0 , 7CD S 879

2 =89 t ( =D:

2 / 7C: 7:7

R :G R . ( 7: R 78D 0 =:M 0 7G9 0 =CG 0 ( =D: 0 , 788 R 8=7 R 2 =:: R ( =DG R 798 798 R 0 798 0 798 R =M= R =M= R 3 797 R 2 G 0 77

8=D $ 1 22 / 8=9 $ / =:= $ =M: 7=M $ 2 / 7D7 $ 78 $ . =DE $ ( C= $ 7M $ 9C 0 - 9C 0 9C 0 / 99 9C

$ 9M 0 M =G07= 0 78 0 9D 0 79 0 ( 9D CE 0 / 7G 0 97 0 1 7M 0 79 0 / 9C 0 78 0 9M $ 98 0 =7C 0 / 8:7 0 2 / 7C8 $ ( :C $ 8=D $ 9M $ D=

0 / 8:8

88:

w w

=M8 =M8 =M9 w / 9= 0 77 9=

0 S 1 879 ==C 7:M / 78D 79= 0 78M 79= 0 , 788 79= 2 / 7CD ( =8M 787 797 =MC / 79C

2 / 7CD

1E:8I 6:

ÑÂÅÄÅÍÈß ÈÇ ÝËÅÌÅÍÒÀÐÍÎÉ ÌÀÒÅÌÀÒÈÊÈ

= > 7 / 7 = / 7 7 3 / 3

* ! 8 1 8 = 3 8 7 )

(

9 = 9 7 H 9 8

C _

D >

C = ! - C 7 C 8 N / C 9 . D = ! - D 7 1

: $ G ` 2 M ) \ > *

C C 7G 7G 89 98 98 98 9M CC CC D= DM :9 :9 GC MC MG ==9 ==9 ==D =7C =7M =89

=E ( 9 ' == 2

=8G

=CE =CE =CE =C9 =DE =D9 =D: =:E =:E =:8 =:9 =:C =GE

> 2 * ) ' =C N 2 / =D ! 2 / =: N =G 1

=MD =MD 7EC 7== 7=9

== = ` == 7 N == 8 $ . == 9 H == C )

=7 '

=7 = =7 7 =7 8 .

=8 Q =9 S

ÑÂÅÄÅÍÈß ÈÇ ÂÛÑØÅÉ ÌÀÒÅÌÀÒÈÊÈ

> ) ' * ' ) + =M H 1 7E 7= ) 77 > 78 +

7=G 7=G 779 78E 797 79D

> A ) ( * ) 0 79 S / 2 7C ! 7D ! 22 / 7: ! 7G

7C= 7C= 7DC 7:7 7GM 8=D

ÎÁÐÀÁÎÒÊÀ ÄÀÍÍÛÕ. ÏÐÈÁËÈÆÅÍÍÛÅ ÂÛ×ÈÑËÅÍÈß. ÒÀÁËÈÖÛ

> 1! ! % ))(- 7M ! . . ;, <

87G

> & ! , ))( ( ) ' 8E ( .

8CM 8CM 8CM 8D8 8DC 8DD 8:= 8:7

H 2 ! .(

8:D 8:D 8G7 9=G 9D9 9GD C7D C7G

8E = $ 1 8E 7 ' - / 2 8E 8 ! + 8E 9 3 ( 8E C S ( . 8E D N / 4 / ( / ; < H . 2 3 2 N + ( 7GE8

& , )

H /

& % )(# 3 0

87G

C7M C7M C8E C8D

Учебное издание Рывкин Альберт Анатольевич Рывкин Анатолий Залманович

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