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),% ( , ' 9 ' . - ( ' ", ! ' 5 F " % % ' 2 # ' " F ' # '( ' % ' 2 '(4 - % ' 2 ! < ' ' 5 (4 ' 5 9 % % ' 2 #' F " , ' 9 ' . - ( ' ", ! ' 5 ),% ( % #.- ' ' $ ! ! ' 5 " # %( ! ! % % < ! ! 5 F # '( #.- '$ ' ! 5 (4 ! 5 ! ! #.- ' '(4 ' '$ ! ' 5 % #% 6 ! 5 9' #. ! ( ' F " S #.- ' ' $ ! ! ' 5 ),% ( ! , ' % " - % #.- ' ' $ , ! '< '.6 5% # 5 - , #' ! , '' < , % , - 1 , ! , ' %

à ë à â à II ÔÓÍÊÖÈÈ

§ 4. Ôóíêöèè è èõ ãðàôèêè 10. ×òî òàêîå ôóíêöèÿ

+ & & + + & + + ? - + , & P' ' $ & % ( - ' $ I,' 2 T % ( -< ' $ 0 % # 5 - 9, & ' + & ' ' + T ' T ' ( 2 ( ( ' - ' % ' 2 % H '' % , ( 2 2 ( T % ( - ' $ 0 ' 9 % # ' , ('.6 % T % ( !' ' 5 0 %

52

53

à ë à â à II

),% ( , ' 9 ' . - ( ' ", ! ' 5 F " % % ' 2 # ' " F ' # '( ' % ' 2 '(4 - % ' 2 ! < ' ' 5 (4 ' 5 9 % % ' 2 #' F " , ' 9 ' . - ( ' ", ! ' 5

§ 4. Ôóíêöèè è èõ ãðàôèêè

10. ×òî òàêîå ôóíêöèÿ

+ & & + + & + +

? -

В се

),% ( ! , ' % " - % #.- ' ' $ , ! '< '.6 5% # 5 - , #' ! , '' < , % , - 1 , ! , ' %

р m на еш at с е em ай бн и т .n е к и ar od .r u

),% ( % #.- ' ' $ ! ! ' 5 " # %( ! ! % % < ! ! 5 F # '( #.- '$ ' ! 5 (4 ! 5 ! ! #.- ' '(4 ' '$ ! ' 5 % #% 6 ! 5 9' #. ! ( ' F " S #.- ' ' $ ! ! ' 5

ÔÓÍÊÖÈÈ

z-

+ , & P' ' $ & % ( - ' $ I,' 2 T % ( -< ' $ 0 % # 5 - 9, & ' + & ' ' +

gd

T ' T '

( 2 ( ( ' - ' % ' 2 % H '' % , ( 2 2 ( T % ( - ' $ 0 ' 9 % # ' , ('.6 % T % ( !' ' 5 0 %

52

53

", ' !' ' $ ", ' % ,9 % !' ' $ I,' 2 0 % ) - 1 - . #.-,7 ' # 1 < - 0 #

),% ( # . % ' - #', ! H 3 ! #, # ( %$ # . # ' % ' # < . L! 33 ! #, #. ( %$ # . # ' % < ' %$ F # . % ' - #', % % # , #' ' # . % ' - #', !

B

0

1

T % ( - ' $ % % ! #% 6 % - T % ( - ' $ % % ! #% 6 % ---------- –

----------- T % ( - ' $ % % ! #% 6 % +

D

– ---------------- T % ( - ' $ % % ! #% 6 %

x

A

11. Âû÷èñëåíèå çíà ÷åíèé ôóíêöèè ïî ôîðìóëå

------

------ –

------ –

------

------

--

------ –

C 1

# $

y

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

---

---

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

------

— 54 —

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

— 55 —

", ' !' ' $ ", ' % ,9 % !' ' $ I,' 2 0 % ) - 1 - . #.-,7 ' # 1 < - 0 #

),% ( # . % ' - #', ! H 3 ! #, # ( %$ # . # ' % ' # < . L! 33 ! #, #. ( %$ # . # ' % < ' %$ F # . % ' - #', % % # , #' ' # . % ' - #', !

B

1

0

–

T % ( - ' $ % % ! #% 6 % ----------- +

D

– ---------------- T % ( - ' $ % % ! #% 6 %

x

В се

------

--

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

z-

------

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

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

------

54

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

---

---

gd

------ –

------ –

------

- T % ( - ' $ % % ! #% 6 % -----------

11. Âû÷èñëåíèå çíà÷åíèé ôóíêöèè ïî ôîðìóëå

------ –

T % ( - ' $ % % ! #% 6 %

A

C 1

# $

y

р m на еш at с е em ай бн и т .n е к и ar od .r u

55

3 %

"

0

+ , , @ + + , , @

T % ( - ' $ 1 5 I,' 2 0 ' , ('. % # : (' / ),% ( 4 % %%' % ' " " % %< %' % ' " H% " % ' " - ,% # : #' + % # , #' ' ' " % %%' % ' "

B

1

----------- %

+ & + + & & & & &

5

y

M 1

x

A

12. Ãðàôèê ôóíêöèè

! " #

y 10

0

1

x

4

y

N

1 0

1

K

x

y 8

1

M

–1 0

56

57

1

5

x

3 %

"

0

+ , , @ + + , , @

/ ),% ( 4 % %%' % ' " " % %< %' % ' " H% " % ' " - ,% # : #' + % # , #' ' ' " % %%' % ' "

4

y

x

12. Ãðàôèê ôóíêöèè

! " #

1 0

1

K

x

z-

N

y 10

0

gd

M 1

A

В се

T % ( - ' $ 1 5 I,' 2 0 ' , ('. % # : ('

B

1

----------- %

+ & + + & & & & &

5

y

р m на еш at с е em ай бн и т .n е к и ar od .r u

1

x

y

8

1

M

–1 0

56

57

1

5

x

---

---

---

---

---

---

y

6

0 1

6

x

y N

1 0

1

x P

% & # '% # # ' F % - ' 9 " I , I,' 2 " & # '% # # ' F " - ' 9 " I , I,' 2 # & # '% # ' # ' F # ' - ' 9 " I , I,' 2 ? - $ - ' 9 " I , I,' 2 ) ' - ' 9 " I , I,' 2 % & # '% # # ' F % - ' 9 " I , " & # '% # # ' F " - ' 9 " I , # & # '% # ' # ' F # ' - ' 9 " I ,

1

— 58 —

x B

M

y

0

3 3

1 1

A

C

1

y

0

) 9 ('. !' ' $ I,' 2 ' - - T 2 ('. !' ' $ I,' 2 ' - -

1

x

— 59 —

---

---

---

---

---

---

y

6

0 1

6

x

N

1

0

1

x

P

% & # '% # # ' F % - ' 9 " I , I,' 2 " & # '% # # ' F " - ' 9 " I , I,' 2 # & # '% # ' # ' F # ' - ' 9 " I , I,' 2 ? - $ - ' 9 " I , I,' 2 ) ' - ' 9 " I , I,' 2

z-

gd

1 0

y

% & # '% # # ' F % - ' 9 " I , " & # '% # # ' F " - ' 9 " I , # & # '% # ' # ' F # ' - ' 9 " I ,

y

— 58 —

x B

M

3 3

1 1

A

C

1

y

0

) 9 ('. !' ' $ I,' 2 ' - - T 2 ('. !' ' $ I,' 2 ' - -

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

Đ’ Ń Đľ

1

x

— 59 —

) " I ,

y

1

10

) I ,

- -----

------

4,7

1 0 1 2,5 " " "

x

m, êã 5

--- --- --- --- =

4

------ --- $ --- % & '(! --- --- --- --- % '

2 1

* ! ' 0 °C + 100 * ! ' 0 + * ! ' 0 + 80 * ! ' 0 60 + + 0 ! 40 ', . + 0 ! 20 ', .

+ 0 ! 0 ', .

– + - -------- -------- -------- --------------------- --- --- --- --- -----

3

0

),% ( " #.6 4 ' . " ,! #.6 4 , ) %< - , ' $ " #.6 4 ' 6 % 4 ' " ,! #.6 % 4 ' P' $ " #.6 < 4 ' % ' (4 % % # , #' ' U " #.6 4 ' . " ,! #.6 0 # # - . #% " # 4 '

1

2

3

4

5

6 V, ë

> $ $ $ = ? # '% # > ' # '

§ 5. Ëèíåéíà ÿ ôóíêöèÿ 13. Ëèíåéíà ÿ ôóíêöèÿ è åå ãðà ôèê V ! # % % ( $# $ %$ ' 5' 5 I,' 2 5

2

4

6

8

10 12 ìèí

? %,6 %I ( 0 ? %I ( 0 ) " 0 ? %,6 %I ( 0 ' @ H 9 ( 0 @ ) " 0 @

— 60 —

6 6 6 U ' 5' 5 $# $ %$ ! # % % ( 6 V ! # % % ( $# $ %$ ' 5' 5 I,' 2 5 N

--- ? ?

— 61 —

) " I ,

y

1

10

) I ,

- -----

------

1 0 1 2,5 m, êã 5

--- --- --- --- =

4

------ --- $ --- % & '(! --- --- --- --- % '

2 1 1

2

3

4

5

6 V, ë

> $ $ $ = ? # '% # > ' # '

В се

§ 5. Ëèíåéíàÿ ôóíêöèÿ

13. Ëèíåéíàÿ ôóíêöèÿ è åå ãðàôèê

V ! # % % ( $# $ %$ ' 5' 5 I,' 2 5

z-

* ! ' 0 °C + 100 * ! ' 0 + * ! ' 0 + 80 * ! ' 0 60 + + 0 ! 40 ', . + 0 ! 20 ', .

+ 0 ! 0 ', .

– + - -------- -------- -------- --------------------- --- --- --- --- -----

3

0

2

4

6

8

10 12 ìèí

? %,6 %I ( 0 ? %I ( 0 ) " 0 ? %,6 %I ( 0 ' @ H 9 ( 0 @ ) " 0 @

60

6 6 6 U ' 5' 5 $# $ %$ ! # % % ( 6

gd

" " "

x

),% ( " #.6 4 ' . " ,! #.6 4 , ) %< - , ' $ " #.6 4 ' 6 % 4 ' " ,! #.6 % 4 ' P' $ " #.6 < 4 ' % ' (4 % % # , #' ' U " #.6 4 ' . " ,! #.6 0 # # - . #% " # 4 '

р m на еш at с е em ай бн и т .n е к и ar od .r u

4,7

V ! # % % ( $# $ %$ ' 5' 5 I,' 2 5 N

--- ? ?

61

---

y

1 1 0

1

0 1

x

y

0 1

x

y

1

1

1 0 1

x

0 1

— 62 —

x

0 1

x

y 1 1 x

1 0 1

y

0 1

x

y

y

0 1

x

1

1

y

y

y

> 1

x

— 63 —

0 1

x

---

1

x

y

x

0 1

1 0 1

— 62 —

y

y

1

1

0 1

x

1 0

0 1

x

y

y

y

x

z-

x

1

gd

0 1

x

0 1

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

1 1 0

0 1

Đ’ Ń Đľ

y

1

1

y

y

y

> 1

1

1 x

x

— 63 —

0 1

x

y

1 0 1

x

y,°C 100

80 * ! ' + * ! 60 ' + N + # ' < 40 " %( ! ' 20 0

1 0 1

70

20 30

40 50

60 x, ìèí

y

10

x

y

60

W I - % %( #

50

3 3 3

---

40

---

30

W I - % %( #

20 10 0 1 –10 –20

— 64 —

3

5

x

---

% W I - 6 ! '',: , " W I - 6 ! '',: , # W I ' - 6 ! '',: , $ W I - 6 ! '',: ,

— 65 —

y

1 0 1

x

y,°C 100

80 * ! ' + * ! 60 ' + N + # ' < 40 " %( ! ' 20

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

0

1 0 1

70

x

y

60 3 3 3

---

40

30

10

–20

— 64 —

60 x, Ïèí

---

---

W I - % %( #

20

0 1 –10

40 50

W I - % %( #

50

z-

20 30

3

Đ’ Ń Đľ

y

10

5

x

% W I - 6 ! '',: , " W I - 6 ! '',: , # W I ' - 6 ! '',: , $ W I - 6 ! '',: ,

gd

— 65 —

# 2

y = –1 y = –5

N $# $ %$ ---

N ?

y = 3,2 y=0

N $# $ %$

1 0 1

x

y = 1,6 y = –1,9

1 0 1

x

y = –2

> > N ( , - # (' 5 - N ( , ' - # (' 5 -

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

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

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

--- ---

---

---

--- ---

--- --- ---

---

---

---

y

1

0

x

–x

67

1 =

y

x

,5 –1

---

66

?

y=

/ ),% ( - # $ " !" # 5 " # $ !" # 5 ($ 0 H% " !" # 5 - ,% # : #' $ + % # , #' '

- # $ " !" # 5 # $ 0 5 ($ 0 5

x

y

+ &

y= 3x

y=7

y=6

14. Ïðÿìàÿ ïðîïîðöèîíàëüíîñòü

=

y

W I ''.6 I,' < 2 5 0 - $ . - < ('. %

y

W I ''.6 I,' < 2 5 0 - $ . - < ('. %

# 2

---

y = 1,6 y = –1,9

1 0 1

x

y = –2

> > N ( , - # (' 5 - N ( , ' - # (' 5 -

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

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

---

---

--- ---

--- ---

--- --- ---

--- ---

---

1

0

— 67 —

1

x

–x

=

y

y

x

---

,5 –1

— 66 —

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

y=

/ ),% ( - # $ " !" # 5 " # $ !" # 5 ($ 0 H% " !" # 5 - ,% # : #' $ + % # , #' '

- # $ " !" # 5 # $ 0 5 ($ 0 5

?

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

x

z-

0 1

gd

y = –5

1

Đ’ Ń Đľ

y = –1

N $# $ %$

N ?

y = 3,2 y=0

N $# $ %$

x

y

+ &

y= 3x

y=7

y=6

14. �ðÿÏà ÿ ïðÎïÎðÜèÎíà ÍßíÎùòß

=

y

W I ''.6 I,' < 2 5 0 - $ . - < ('. %

y

W I ''.6 I,' < 2 5 0 - $ . - < ('. %

1

0 y= 2,5x

x

y= –0 ,5

x

1 0

y

10

5

0 1

1

x

%

---

1 0

-

1

x

%

) ' 9 "

? - ' 9 "

--- ---

---

? - ' 9

— 68 —

x

) 4 6 . # -, # % - % ) 4 6 - # % - % + % ( - 4 6 @ # % - % @ H % - % - 6 ! # ! (< 4 - 4 - 4 6 % XY - ' 9 " I , " ) ' 9 " I , # ) ' 9 " I , $ ) ' 9 " I ,

y

5

) *

P # % % ( - < 9 '' ! I ,

- - - P' ' - %,7 % #,

y

1

4,5x y=–

y

) ' 9

— 69 —

1

0 y= 2,5x

x

y= –0 ,5

x

1 0

1

x

Đ’ Ń Đľ

% XY - ' 9 " I , " ) ' 9 " I , # ) ' 9 " I , $ ) ' 9 " I ,

---

1 1

x

? - ' 9 "

---

? - ' 9

— 68 —

%

) ' 9 "

--- ---

-

5

x

) 4 6 . # -, # % - % ) 4 6 - # % - % + % ( - 4 6 @ # % - % @ H % - % - 6 ! # ! (< 4 - 4 - 4 6

%

0

10

) *

y

y

0 1

z-

5

- - - P' ' - %,7 % #,

P # % % ( - < 9 '' ! I ,

y

1

4,5x y=–

gd

y

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

) ' 9

— 69 —

#

#

---

---

? - ' 9

$ --- ---

$ --- ---

--- ---

0

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

--- --- --- $ --- ---

? - ' 9 )

? - ' 9 )

---

y

1 x

0 1

x

>

0

1

1 1

x

0 1

x

>

=

--- =

-- - >

15. Âçà èìíîå ðà ñïîëîæåíèå ãðà ôèêîâ ëèíåéíûõ ôóíêöèé W I - ('. W I - % : %$ W I - % : %$

— 70 —

x

=

y

y

1

0

x

33 = --- 333 > --- --- --- 3Z > ---

y

1 0 1

1

3 = ---

1

) ' 9

) ' 9

>

y

1

--- ---

y

? - ' 9

=

W I - % : %$ W I - ('. W I - % : %$

— 71 —

? - ' 9

$ --- ---

$ --- ---

0

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

--- --- --- $ --- ---

? - ' 9 )

? - ' 9 )

---

) ' 9

y

1 0 1

1 x

0 1

x

>

=

--- =

-- - >

z-

>

0

1

1 1

x

x

0 1

x

15. Âçàèìíîå ðàñïîëîæåíèå ãðàôèêîâ ëèíåéíûõ ôóíêöèé

W I - ('. W I - % : %$ W I - % : %$

70

1

=

y

y

0

x

1

33 = --- 333 > --- --- --- 3Z > ---

y

1

3 = ---

) ' 9

y

1

--- ---

--- ---

>

gd

y

? - ' 9

=

р m на еш at с е em ай бн и т .n е к и ar od .r u

---

---

#

В се

#

W I - % : %$ W I - ('. W I - % : %$

71

) % : %$

–x +

y = –x – 1,5 y y = 0,5x + 2,5 y = 2,5

6

=

x

3

1

–

— 72 —

0

–x

) % : %$

) % : %$

y

1 =

1 0 1

x

y = x + 2,5 y = –x + 2,5

y

y = 3x

1

— 73 —

0

1

y= 3x – 4

3 0 ' . - % ' $ 0 ' . - % ' $ 0 ' . - % ' $ 0 ' . - % ' $ 0 ' . - % ' $ 0 ' . - % ' $

–x

y

y =

---

? - % : %$

y

---

y= 3x + 1,2

W I - ('. , I,' 2 5 W I - % : %$ , I,' 2 5

x

= –x

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

y

y = 0,5x + 2,5

y = 2,5

1

x

y = –x – 1,5

6

+

1

3

0

–

— 72 —

–x

0 1

x

y = x + 2,5 y = –x + 2,5

z-

y

1

— 73 —

0

y= 3x + 1,2

y = 3x

1

y= 3x – 4

gd

) % : %$

) % : %$

1

=

3 0 ' . - % ' $ 0 ' . - % ' $ 0 ' . - % ' $ 0 ' . - % ' $ 0 ' . - % ' $ 0 ' . - % ' $

y

y

y

–x

---

=

) % : %$

y

--- ? - % : %$

Đ’ Ń Đľ

W I - ('. , I,' 2 5 W I - % : %$ , I,' 2 5

x

2

0 1

x

>

------ > =

> =

–x –

2

y

y= 17x + 20

40

y 0x y = –3

50

30 20 10 0 1

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå II Ê ïàðàãðàôó 4 - ---------

50

" > M M T % ( - ' $ 0 #% M M =

40

------ @ , +--

30

&

10 x

–20

–20

–30

–30

–40

–40

74

0x + 8 y = –3

0 1 –10

' 0 - #.5 - # ' 0 # 5 0 ! - #.5 % 0 ! - % ' 5 0 ' - #. 0 ' # .

20

–10 y= 17x

33 >

=

W I %- 9 ' # 3 333 ' '.6 < # $6 W I %- 9 ' # 33 3Z ' '.6 < # $6

=

y

–2 ,4x 0 y=

1

),% ( # 3 '( ! # ! ! ' # 33 0 ! ' H% " ! # !

! ' - ,% # : #'

# 3 '( ! # ! ! '

–

3 =

x

y

=

y

x

' ! # % $ - '' $ ! # % $ - - -

75

2

0 1

x

–x – 2

y

y= 17x + 20

30 20 10 0 1

- ---------

" > M M T % ( - ' $ 0 #% M M =

50 40

------ @ , +--

30

10 x

–20

–20

–30

–30

–40

–40

74

0x + 8 y = –3

0 1 –10

&

' 0 - #.5 - # ' 0 # 5 0 ! - #.5 % 0 ! - % ' 5 0 ' - #. 0 ' # .

20

–10 y= 17x

Ê ïàðàãðàôó 4

x

gd

40

y 0x y = –3

50

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå II

В се

------ > =

> =

W I %- 9 ' # 3 333 ' '.6 < # $6 W I %- 9 ' # 33 3Z ' '.6 < # $6

р m на еш at с е em ай бн и т .n е к и ar od .r u

=

>

y

–2 ,4x 0 y=

z-

1

),% ( # 3 '( ! # ! ! ' # 33 0 ! ' H% " ! # !

! ' - ,% # : #'

# 3 '( ! # ! ! '

–

3 = = 33 >

x

y

=

y

' ! # % $ - '' $ ! # % $ - - -

75

+ - -------

–---------------------

+ - -------

–--------------------

+ - -------

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

y

H% % H% %

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

1 0

1

–2 0 2

— 76 —

12

x

x

1

---

1 –2

5

0

x

y

y

1

–2

x

–14

+

-----------

---

–2 1 0 2

–10

y

) ) > > ) > =

— 77 —

ั m ะฝะฐ ะตั at ั ะต em ะฐะน ะฑะฝ ะธ ั .n ะต ะบ ะธ ar od .r u

+ - -------

โ ---------------------

+ - -------

โ --------------------

+ ----------------- -------

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

1 โ 2 0 2

ย 76 ย

x

1 โ 2

x

5

z-

12

x

y

1 0

gd

1

โ 2

ะ ั ะต

y

0

---

1

y

H% % H% %

x

โ 14

+

-----------

---

โ 2 1 0 2

โ 10

y

) ) > > ) > =

ย 77 ย

8% % 8% %

),% (

) !' ' I,' 2 #' !' ' : ", ' ),% (

V, ë 25 20 15 10 5 0

------ ---

2

4

6

8

H, ñì

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78

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V, ë 25 20 15 10 5 0

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р m на еш at с е em ай бн и т .n е к и ar od .r u

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Ê ïàðàãðàôó 5

В се

------ @ + '$$ % % ( ' ' -, <

$ 9

) !' ) % ( , - L

+ '$$ % % ( ' -, , --- ---

V ' 5' $ I,' 2 $

79

y

1

x 0 1

G ' . - % ' $ " I % %$ < ' - -

y

500 400 300 200 100

5 4 3 2 1

0

2 3 4

x

F % - ' 9 " I , % ---

---

1

9 - ' ( 2 . !' ' $

200 400 0 100 300 x

% W I - 6 ! , % 4 W I - 6 ! , 4

–1 0 1

x

êì 75

60

P # % - % - < ! ' ? -, ( # # % < - % ! ' & [ & [

— 80 —

y

y

1

6 W I ' - 6 ! , 6 7 W I ' - 6 ! , 7

45 30 15 0

1

2

3

4

5

, @% , @%

) % 0 ' . - % ' $ ) % 0 ' . - % ' $ ) % 0 ' . - % ' $

— 81 —

÷

y

1

x 0 1

G ' . - % ' $ " I % %$ < ' - -

y

500 400 300 200 100

5 4 3 2 1

0

2 3 4

x

---

---

y

1

9 - ' ( 2 . !' ' $

y

1

F % - ' 9 " I , %

200 400 0 100 300 x

–1 0 1

x

ĂŞĂŹ 75

Đ’ Ń Đľ

6 W I ' - 6 ! , 6 7 W I ' - 6 ! , 7

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

60

P # % - % - < ! ' ? -, ( # # % < - % ! '

45

30 15

0

1

2

3

4

5

% W I - 6 ! , % 4 W I - 6 ! , 4

— 80 —

gd

z-

& [ , @% & [ , @%

) % 0 ' . - % ' $ ) % 0 ' . - % ' $ ) % 0 ' . - % ' $

— 81 —

á

0 ' . - % ' $ 0 ' . - % ' $

) % 0 ' . - % ' $ ? - % ? - %

y

y y =

y= ax x

1 1 0

x

= y 5 F 5 - ' 9 " I , F - $ $ - (' " I , I,' 2 I,' 2 $ ! %$ I , 5 ) % ( , - $ $ - 6 < ! % T ' ('

y

1 0 1

? ' 9 #', ," ('

A(2; 3) 0

1

x

0 ' . - % ' $ 0 ' . - % ' $

— 82 —

x

y = –2x + 3

y

1

y = 3x + 2

y = 0,5x – 2

ax

0 1

bx

1

bx y=

— 83 —

0 ' . - % ' $ 0 ' . - % ' $

y y =

x

1 1 0

x

= y

y

A(2; 3) 1 0

1

x

0 ' . - % ' $ 0 ' . - % ' $

ย 82 ย

y = 3x + 2

y = 0,5x โ 2

5 F 5 - ' 9 " I , F - $ $ - (' " I , I,' 2 I,' 2 $ ! %$ I , 5 ) % ( , - $ $ - 6 < ! % T ' ('

y

1 0 1

x

y = โ 2x + 3

? ' 9 #', ," ('

z-

y= ax

ax

0 1

bx

1

bx y=

gd

y

ะ ั ะต

ั m ะฝะฐ ะตั at ั ะต em ะฐะน ะฑะฝ ะธ ั .n ะต ะบ ะธ ar od .r u

) % 0 ' . - % ' $ ? - % ? - %

ย 83 ย

à ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

§ 6. Ñòåïåíü è åå ñâîéñòâà 16. Îïðåäåëåíèå ñòåïåíè ñ íàòóðàëüíûì ïîêàçàòåëåì --- --- --- --- ---

!

!

--- --- %' # ' 0 - ! (

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

-

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

0 %' # ' 0 - ! ( 0 %' # ' 0 - ! ( 0 %' # ' 0 - ! (

0 %' # ' 0 - ! (

84

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

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0 %' # ' 0 - ! (

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

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

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

-

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

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

85

ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

§ 6. Ñòåïåíü è åå ñâîéñòâà 16. Îïðåäåëåíèå ñòåïåíè ñ íàòóðàëüíûì ïîêàçàòåëåì --- --- --- --- ---

!

!

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

-

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

0 %' # ' 0 - ! ( 0 %' # ' 0 - ! ( 0 %' # ' 0 - ! (

0 %' # ' 0 - ! (

84

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

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-

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z-

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

gd

--- --- %' # ' 0 - ! (

В се

0 %' # ' 0 - ! (

р m на еш at с е em ай бн и т .n е к и ar od .r u

à ë à â à III

85

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= > - 1 , > > = - 1 , > = > - 1 , =

— 86 —

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

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---

)

)

)

)

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— 87 —

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= > - 1 , > > = - 1 , > = > - 1 , =

ย 86 ย

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

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ั m ะฝะฐ ะตั at ั ะต em ะฐะน ะฑะฝ ะธ ั .n ะต ะบ ะธ ar od .r u

---

z-

)

)

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gd

ะ ั ะต

ย 87 ย

) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )

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— 88 —

G# %, . % +, # # % G# !' % % & !' % ( # # % G, !' % % +, , # %

; # ''.5 # !' % % ; '' $ %, # # %

) ) )

0 ' . - % ' $ 0 ' . - % ' $ W I - ('. W I - % : %$

17. Óìíîæåíèå è äåëåíèå ñòåïåíåé

' ' '

— 89 —

) ) ) ) ) ) ) ) ) ) ) )

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88

W I - ('. W I - % : %$

17. Óìíîæåíèå è äåëåíèå ñòåïåíåé

z-

0 ' . - % ' $ 0 ' . - % ' $

' ' '

gd

В се

) )

G# %, . % +, # # % G# !' % % & !' % ( # # % G, !' % % +, , # %

; # ''.5 # !' % % ; '' $ %, # # %

) ) )

р m на еш at с е em ай бн и т .n е к и ar od .r u

) ) ) ) ) )

89

' ' ' ' '

' ' '

– ----------------- –

--- -------------- - --- --- --- --- --- – --- ---------

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— 90 —

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---------

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---

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— 91 —

' ' ' ' '

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โ

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

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ย 90 ย

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z-

----------

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ั m ะฝะฐ ะตั at ั ะต em ะฐะน ะฑะฝ ะธ ั .n ะต ะบ ะธ ar od .r u

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ย 91 ย

18. Âîçâåäåíèå â ñòåïåíü ïðîèçâåäåíèÿ è ñòåïåíè

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

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

y

1

0 1

8% 8% + , & + & & ' &

+ + +

- : = > % F % - ' 9 " I , " F " - ' 9 " I , % G,% " ' \ % # % " G,% " ' \ % # % "

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

----------------------------- "

— 92 —

x

! !

),% ( % ' # F " - 7 ( # 8% % ' # #' ) 7 ( ,# %$ # ! 0 % ' # ) 7 ( ,# < %$ # ! + ' # 0 ) 7 ( ,# < %$ # ! + ' # 0 ) 7 ( ,# < %$ # !

),% ( , F " " \ T \ ,# %$ # !

— 93 —

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

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y

1

0 1

8% 8% + , & + & & ' &

+ + +

- : = > % F % - ' 9 " I , " F " - ' 9 " I , % G,% " ' \ % # % " G,% " ' \ % # % "

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

----------------------------- "

92

x

р m на еш at с е em ай бн и т .n е к и ar od .r u

! !

),% ( % ' # F " - 7 ( # 8% % ' # #' ) 7 ( ,# %$ # ! 0 % ' # ) 7 ( ,# < %$ # ! + ' # 0 ) 7 ( ,# < %$ # ! + ' # 0 ) 7 ( ,# <

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18. Âîçâåäåíèå â ñòåïåíü ïðîèçâåäåíèÿ è ñòåïåíè

gd

В се

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),% ( , F " " \ T \ ,# %$ # !

93

T \ ,# %$ # !

T \ ,# %$ # !

T \ ,# %$ # !

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— 94 —

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

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

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> > = = = % ) ) ) - -

— 95 —

T \ ,# %$ # !

T \ ,# %$ # !

! !

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

---

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ั m ะฝะฐ ะตั at ั ะต em ะฐะน ะฑะฝ ะธ ั .n ะต ะบ ะธ ar od .r u

T \ ,# %$ # !

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%

z-

gd

ย 94 ย

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§ 7. Îäíî÷ëåíû 19. Îäíî÷ëåí è åãî ñòàíäàðòíûé âèä

N

?

N ?Y

N

N

? N

N N

N N

%

N

?

?

N

N

?

J ' % N ' % H.% % %

G 1II 2 ' G 1II 2 ' G 1II 2 ' G 1II 2 ' --- --- G 1II 2 '

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

+ - '( + - '(

+ - '( [ - '(

+ - '( + - '(

T ' . 0 - # - 9'. % " Q %2 %%. 0 - # - 9'. % " G ' . 0 - # - 9'. % " ---

G 1II 2 ' '( '( ' (

---

---

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– -

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

96

–

---

–

97

§ 7. Îäíî÷ëåíû 19. Îäíî÷ëåí è åãî ñòàíäàðòíûé âèä

N ?Y

N

N

? N

N N

N N

%

N

?

?

N

N

?

J ' % N ' % H.% % %

G 1II 2 ' G 1II 2 ' G 1II 2 ' G 1II 2 ' --- --- G 1II 2 '

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

+ - '( + - '(

+ - '( [ - '(

+ - '( + - '(

T ' . 0 - # - 9'. % " Q %2 %%. 0 - # - 9'. % " G ' . 0 - # - 9'. % " ---

G 1II 2 ' '( '( ' (

---

В се

р m на еш at с е em ай бн и т .n е к и ar od .r u

N

?

---

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96

z-

--- ---

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gd

– -

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

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97

–

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

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20. Óìíîæåíèå îäíî÷ëåíîâ. Âîçâåäåíèå îäíî÷ëåíà â ñòåïåíü

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

--- ---

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— 98 —

S

--- ---

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— 99 —

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

20. Óìíîæåíèå îäíî÷ëåíîâ. Âîçâåäåíèå îäíî÷ëåíà â ñòåïåíü

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98

S

р m на еш at с е em ай бн и т .n е к и ar od .r u

--- ---

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gd

В се

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

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--- --- ---

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--- ' ( ( ' (

— 100 —

! # ! #! " #!

' ( '( ' ( ' ( ' ( ' ( - ------ ------ ----

),% ( ' 5 -,% ," ( K.

+

T -,%

3 %

33 %

--- ---

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P' $ ' 33 % ," $ , # - ! (4 % % # , #' '

! ' 5 ),% ( ! ' 5 # 3 , # ! I $ '(4 # 33 K.

+

) # !

3 6 ' 7

33 6 ' 7

P' $ # 3 6 ' 7 I $ , # ! '(< 4 # 33 % % # , #' '

! ' 5 % "

— 101 —

---

! # ! #! " #!

' ( '( ' ( ' ( ' ( ' ( - ------ ------ ----

---

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--- '( ' ( --- ' ( ' (

--- ' ( ( ' (

ย 100 ย

K.

+

T -,%

3 %

33 %

P' $ ' 33 % ," $ , # - ! (4 % % # , #' '

! ' 5

),% ( ! ' 5 # 3 , # ! I $ '(4 # 33 K.

+

) # !

3 6 ' 7

33 6 ' 7

P' $ # 3 6 ' 7 I $ , # ! '(< 4 # 33 % % # , #' '

z-

),% ( ' 5 -,% ," (

gd

ะ ั ะต

--- ---

ั m ะฝะฐ ะตั at ั ะต em ะฐะน ะฑะฝ ะธ ั .n ะต ะบ ะธ ar od .r u

--- --- ---

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! ' 5

% "

ย 101 ย

0 ' . - % ' $ T ' . 0 - # - 9'. % Q %2 %%. 0 - # - 9'. % G ' . 0 - # - 9'. %

21. Ôóíêöèè O = N2 è O = N3 è èõ ãðà ôèêè

- -

- - > ' - - = ' - -

- - = ' - - > ' - -

— 102 —

),% ( % ' # % " - 7 ( % 8% % ' # % - 7 ( % ) 7 ( ,# %$ # !

- % - 7 ( --------- % 8% % ' # ----

) 7 ( , '(4 %$ # !

* . - 7 ( ,# %( # ! % ', ' ,# < ( # ! * . - 7 ( ,# %( # ! % ', ' ,# < ( # !

- -

- - > > ' - - 8% , ,# ( # ! \ ,# %$ # ! 8% , , '(4 ( # ! \ , '(4 %$ # ! & , ' ,# ( # !

y

1 0

-

— 103 —

1

x

- -

- - > ' - - = ' - -

- - = ' - - > ' - -

102

) 7 ( , '(4 %$ # !

* . - 7 ( ,# %( # ! % ', ' ,# < ( # ! * . - 7 ( ,# %( # ! % ', ' ,# < ( # !

р m на еш at с е em ай бн и т .n е к и ar od .r u

21. Ôóíêöèè O = N2 è O = N3 è èõ ãðàôèêè

- -

- - > > ' - -

8% , ,# ( # ! \ ,# %$ # ! 8% , , '(4 ( # ! \ , '(4 %$ # ! & , ' ,# ( # !

y

z-

- % - 7 ( --------- % 8% % ' # -----

1 0

gd

T ' . 0 - # - 9'. % Q %2 %%. 0 - # - 9'. % G ' . 0 - # - 9'. %

),% ( % ' # % " - 7 ( % 8% % ' # % - 7 ( % ) 7 ( ,# %$ # !

В се

0 ' . - % ' $

-

103

1

x

%

F % - ' 9 " I ,

0 ' . - % ' $

" --- ---

F " - ' 9 " I ,

M M M M M M M M M M M M M M M M

- # --- ----

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

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--- ----

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F # ' - ' 9 " I ,

y

§ 8. Àáñîëþòíà ÿ è îòíîñèòåëüíà ÿ ïîãðåøíîñòè

=

22. Àáñîëþòíà ÿ ïîãðåøíîñòü

1 0

>

1

x

>

) 7 ( - ,# %$ # ! - 1 , % - 5< "

M M

M M

M M M M

M M

M M

T \ ,# %$ # ! - 1 , # ' - , %$ '

M M M M M M

> = > > = >

M M M M M M M

M

— 104 —

— 105 —

%

F % - ' 9 " I ,

0 ' . - % ' $

" --- ---

- # --- ----

-

--- ----

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F # ' - ' 9 " I ,

y

§ 8. Ă€åùÎÍÞòíà ÿ è ÎòíÎùèòüÍßíà ÿ ïÎãðüøíÎùòè

=

22. Ă€åùÎÍÞòíà ÿ ïÎãðüøíÎùòß

1 0

>

1

x

>

) 7 ( - ,# %$ # ! - 1 , % - 5< " T \ ,# %$ # ! - 1 , # ' - , %$ ' > = > > = >

— 104 —

M M

M M

M M

M M

M M

M M

z-

M M M M M M

M M M M M M M

M

gd

Đ’ Ń Đľ

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

F " - ' 9 " I ,

M M M M M M M M M M M M M M M M

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

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— 105 —

---

–

--- --- ------ --------------- ------ ------ –

--- --- --------- --------------------- --------- --------- –

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

–

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

%"# 584 % ' % (: 2 .6 %5" % ' % (: 2 .6

A

M

B

0 4 '" '2 , 0 %$ .6 0 ' 5 5 0 2 .6 0 0 % .6 + - ------ M M > ----------

) 9 ' #. ' % ' % (: " --- ---

---

– -------- > --------- --------------------------- - – - -------- --------- --- ------------------------------

--------- --------- --------- 0 - 9 '' !' ' % --

% ' % (:

),% ( , % . 4 - 4 " ' # ,% 6 ) 4 ' -, ( ' # ,% - 6 P' $ # %( -, ( % % # , #' ' , % . 4 - 4

106

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

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

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

3 4 ' . # -, ' 33 4 ' . # -, ' 3 4 ' ' # 9 ' '(4 @ 0 % % ( 3 4 '. @ 0 % % ( 33 4 '. 33 4 ' - . # " '(4 F - % ' $ " I # !' 4 '. #% %( ! - % ' # 9 ' $ 3 4 '. ' %% $' %

23. Îòíîñèòåëüíàÿ ïîãðåøíîñòü ------- ------- / M M ------- / ----------- / M M M M ------- /

---

M M

M M

-------------- /

- -----

M M

----------------- /

– ------------------------------- -------------- /

----------- /

----------- /

M M M M

107

---

%"# 584 % ' % (: 2 .6 %5" % ' % (: 2 .6

A

M

B

0 4 '" '2 , 0 %$ .6 0 ' 5 5 0 2 .6 0 0 % .6 + - ------ M M > ----------

) 9 ' #. ' % ' % (: " --- ---

---

– -------- > --------- --------------------------- - – - -------- --------- --- ------------------------------

--------- --------- --------- 0 - 9 '' !' ' % --

% ' % (:

),% ( , % . 4 - 4 " ' # ,% 6 ) 4 ' -, ( ' # ,% - 6 P' $ # %( -, ( % % # , #' ' , % . 4 - 4

— 106 —

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

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

3 4 ' . # -, ' 33 4 ' . # -, ' 3 4 ' ' # 9 ' '(4 @ 0 % % ( 3 4 '. @ 0 % % ( 33 4 '. 33 4 ' - . # " '(4 F - % ' $ " I # !' 4 '. #% %( ! - % ' # 9 ' $ 3 4 '. ' %% $' %

Ń€ m на ĐľŃˆ at Ń Đľ em Đ°Đš йн и Ń‚ .n Đľ Đş и ar od .r u

23. ĂŽòíÎùèòüÍßíà ÿ ïÎãðüøíÎùòß

------- ------- / M M ------- / ----------- / M M M M ------- /

---

M M

M M

-------------- /

- -----

M M

----------------- /

z-

gd

–

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

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Đ’ Ń Đľ

–

--- --- ------ --------------- ------ ------ –

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

– ------------------------------- -------------- /

----------- /

----------- /

M M M M

— 107 —

------- /

–

------- / -----------------------

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----------- / ------------------- /

H ! ' ' " " " "

------------ / ------------ /

H ! ' '

Q %2 %% % '(4 %2 %%. " # !

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

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

0 ' . - % ' $ % %(: 2 %% 0 ' . - % ' $ % %(: '

Äîïîëíèòåëüíûå óïðàæíåíèÿ ê ãëàâå III Ê ïàðàãðàôó 6 & # '% # ' # ' & # '% # # ' ) % ( , - # !# ' % # # < - , % ' # :7 %$ ' T %: % , 9 ' # %$ 2 I 5

108

F ' # %$ 2 I 5 ) % 9 ' % - , % ' # :< 7 %$ ' - % ( , T% %( ! ( ' # %$ ' ) 1 , % ' # %$ ', !' < %$ '

= = > = >

> =

> = ' = ' = '

= '

109

- / ------------

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H ! ' '

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108

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— 110 —

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— 113 —

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— 113 —

Ê ïàðàãðàôó 7

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118

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119

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— 121 —

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25. Ñëîæåíèå è âû÷èòàíèå ìíîãî÷ëåíîâ

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