решение задач из учебн алгебра 7кл макарычева, миндюк и др 2005 288с

y = kx + b an . ak = an

+k

an : ak = an

-k

Решение задач

(a n)k = a nk (a - b)(a + b) = a 2 - b 2

Из учебника Ю. Н. Макарычева, Н. Г. Миндюк, К. И. Нешкова, С. Б. Суворовой

«Алгебра. 7 класс»

(a - b) 2 = a 2 - 2ab + b 2

(М.: Просвещение, 2004)

(a + b) 2 = a 2 + 2ab + b 2 a 3 + b 3 = (a + b)(a 2 - ab + b 2) y = kx + b an . ak = an

+k

an : ak = an

-k

(a n)k = a nk (a - b)(a + b) = a 2 - b 2

Москва ОНИКС Мир и Образование 2005

УДК 512(076.2) ББК 22.14 Р47

Автор-составитель Н. Д. Луканов

Решение задач из учебника Ю. Н. Макарычева, Н. Г. МинР47 дюк, К. И. Нешкова, С. Б. Суворовой «Алгебра. 7 класс» / Авт.-сост. Н. Д. Луканов. — М.: ООО «Издательство Оникс»: ООО «Издательство «Мир и Образование», 2005. — 288 с.: ил. ISBN 5-488-00120-4 (ООО «Издательство Оникс») ISBN 5-94666-237-6 (ООО «Издательство «Мир и Образование»)

Пособие содержит решения всех задач из последнего издания учебника Ю. Н. Макарычева, Н. Г. Миндюк, К. И. Нешкова, С. Б. Суворовой «Алгебра. 7 класс», включая и задач и повышенной трудности. Оно будет полезно ученикам и их родителям при проверке домашних заданий и незаменимо в тех случаях, если ученику приходится заниматься самостоятельно. УДК 512(076.2) ББК 22.14 ISBN 5-488-00120-4 (ООО «Издательство Оникс») ISBN 5-94666-237-6 (ООО «Издательство «Мир и Образование») © ООО «Издательство «Мир и Образование», 2005 © Оформление обложки. ООО «Издательство Оникс», 2005

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11. Âû÷èñëåíèå çíà ÷åíèé ôóíêöèè ïî ôîðìóëå

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

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11. Âû÷èñëåíèå çíà ÷åíèé ôóíêöèè ïî ôîðìóëå

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+ , , @ + + , , @

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

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1

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+ & + + & & & & &

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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

+ , , @ + + , , @

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

B

1

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

+ & + + & & & & &

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y

M 1

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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

---

---

---

---

---

---

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 —

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---

---

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 —

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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 ,

- -----

------

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 —

---

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

---

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

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 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 —

# 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 -

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

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

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---

---

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---

y

1

0

67

1

x

–x

=

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 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 -

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

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

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---

---

--- ---

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---

y

1

0

67

1

x

–x

=

y

x

---

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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 - $ . - < ('. %

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

— 68 —

) ' 9 "

--- ---

-

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

y

10

5

0 1

1

x

%

---

1 0

1

x

%

? - ' 9 "

---

? - ' 9

— 68 —

) ' 9 "

--- ---

-

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 —

#

---

---

#

? - ' 9

$ --- ---

$ --- ---

0

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

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

? - ' 9 )

? - ' 9 )

---

) ' 9

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 = ---

y

1

) ' 9

>

y

1

--- ---

--- ---

y

? - ' 9

=

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

— 71 —

#

---

---

#

? - ' 9

$ --- ---

$ --- ---

0

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

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? - ' 9 )

? - ' 9 )

---

) ' 9

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 = ---

y

1

) ' 9

>

y

1

--- ---

--- ---

y

? - ' 9

=

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

— 71 —

) % : %$

+

x

y = –x – 1,5 y y = 0,5x + 2,5 y = 2,5

6

–x

=

1

3

— 72 —

0 –

) % : %$

) % : %$

y

–x

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 ' . - % ' $

1 =

–x

y

y =

---

y

--- ? - % : %$

y= 3x + 1,2

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

x

) % : %$

+

x

y = –x – 1,5 y y = 0,5x + 2,5 y = 2,5

6

–x

=

1

3

— 72 —

0 –

) % : %$

) % : %$

y

–x

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 ' . - % ' $

1 =

–x

y

y =

---

y

--- ? - % : %$

y= 3x + 1,2

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

=

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 = = 33 >

x

y

=

y

x

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

75

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

=

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 = = 33 >

x

y

=

y

x

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

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 —

+ - -------

–---------------------

+ - -------

–--------------------

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

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 —

8% % 8% %

),% (

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

V, ë 25 20 15 10 5 0

------ ---

H, ñì 2

4

6

8

) --- !' ' I,' 2 - # - 9' !' ' :

10 12 14 16

", ' T ! T ! . # 4 ' 0 9 . . # ' ! * ! - % #.6 ! . # . ' %< % $' ? %% $' ' . ! - % #.6 ' -, , ! - % #.6 ' -,< '

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

$ 9

– ----------------

E# $ %$

E# $ %$ ? $# $ %$ E# $ %$

E# $ %$ E# $ %$

) !' ) % ( , - L

Ê ïàðàãðàôó 5

) !' ) % ( , - L

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

78

) - - ) 1 , ) # # - 1 , I , , , 9 %$ ' # '

V ' 5' $ I,' 2 $

79

8% % 8% %

),% (

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

V, ë 25 20 15 10 5 0

------ ---

H, ñì 2

4

6

8

) --- !' ' I,' 2 - # - 9' !' ' :

10 12 14 16

", ' T ! T ! . # 4 ' 0 9 . . # ' ! * ! - % #.6 ! . # . ' %< % $' ? %% $' ' . ! - % #.6 ' -, , ! - % #.6 ' -,< '

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

$ 9

– ----------------

E# $ %$

E# $ %$ ? $# $ %$ E# $ %$

E# $ %$ E# $ %$

) !' ) % ( , - L

Ê ïàðàãðàôó 5

) !' ) % ( , - L

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

78

) - - ) 1 , ) # # - 1 , I , , , 9 %$ ' # '

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 , % ---

---

y

1

9 - ' ( 2 . !' ' $

y

1

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

200 400 0 100 300 x

–1 0 1

x

êì 75

60

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

45 30 15 0

1

2

3

4

5

& [ , @% & [ , @% % W I - 6 ! , % 4 W I - 6 ! , 4

— 80 —

) % 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

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

---

y

1

9 - ' ( 2 . !' ' $

y

1

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

200 400 0 100 300 x

–1 0 1

x

êì 75

60

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

45 30 15 0

1

2

3

4

5

& [ , @% & [ , @% % W I - 6 ! , % 4 W I - 6 ! , 4

— 80 —

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

— 81 —

÷

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 ' . - % ' $

) % 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 —

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

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

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

0 %' # ' 0 - ! (

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

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85

à ë à â à III ÑÒÅÏÅÍÜ Ñ ÍÀÒÓÐÀËÜÍÛÌ ÏÎÊÀÇÀÒÅËÅÌ

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

!

!

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

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

0 %' # ' 0 - ! (

84

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— 86 —

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— 88 —

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

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

) ) )

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

17. Óìíîæåíèå è äåëåíèå ñòåïåíåé

' ' '

— 89 —

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

) )

- : ' $ % - '( : " % % ( % ' 2 (' = % # (' - : - : ' $ % - '( : " % % ( % ' 2 (' = - : 1 %, ' 2 (< ' " % - 9 (' " Q' " ' = - :

— 88 —

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

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

) ) )

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17. Óìíîæåíèå è äåëåíèå ñòåïåíåé

' ' '

— 89 —

' ' ' ' '

' ' '

– ----------------- –

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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 —

18. Âîçâåäåíèå â ñòåïåíü ïðîèçâåäåíèÿ è ñòåïåíè

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

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

y

1

0 1

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

+ + +

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

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

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

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x

! !

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

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

— 93 —

T \ ,# %$ # !

T \ ,# %$ # !

T \ ,# %$ # !

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T \ ,# %$ # !

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

N

?

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

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

+ - '( + - '(

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+ - '( + - '(

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96

–

97

–

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

N

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

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

+ - '( + - '(

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

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

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— 100 —

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

+

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+

) # !

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33 6 ' 7

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— 101 —

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+

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33 6 ' 7

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— 101 —

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

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

- -

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— 102 —

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

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y

1 0

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— 103 —

1

x

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

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

- -

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— 102 —

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

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y

1 0

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— 103 —

1

x

%

F % - ' 9 " I ,

0 ' . - % ' $

" --- ---

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

- # --- ----

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y

§ 8. Àáñîëþòíà ÿ è îòíîñèòåëüíà ÿ ïîãðåøíîñòè

=

22. Àáñîëþòíà ÿ ïîãðåøíîñòü

1 0

>

1

x

>

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

- # --- ----

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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 —

---

–

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

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

---

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% ' % (:

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106

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

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

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

---

M M

M M

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

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

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107

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106

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

---

M M

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

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107

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

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

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

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

108

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

= = > = >

> =

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109

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

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

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

108

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

= = > = >

> =

> = ' = ' = '

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109

= = = > >

>

H % , $6 - : ' , (' %, 2 I % $ , ' - 1 , % ' ' $ % < $ ' #% " , $# $ (%$ ' , ('. % 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( = = - : % # (' , #' ' ' ' 5 = - : % # (' , #' ' ' ' 5

— 110 —

P' ' '' " #. 9 ' $ #' - ) = # $ % ( , #' ' $ - 9 (' ' #' ) 1 , - 9 ('.6 ' 5 ' ? - > # $ % ( , #' ' $ - 9 ('

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

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— 111 —

= = = > >

>

H % , $6 - : ' , (' %, 2 I % $ , ' - 1 , % ' ' $ % < $ ' #% " , $# $ (%$ ' , ('. % 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( 0 '( = = - : % # (' , #' ' ' ' 5 = - : % # (' , #' ' ' ' 5

— 110 —

P' ' '' " #. 9 ' $ #' - ) = # $ % ( , #' ' $ - 9 (' ' #' ) 1 , - 9 ('.6 ' 5 ' ? - > # $ % ( , #' ' $ - 9 ('

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

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8% ,% ," ,# ( # ! - 7 ( ,# < %$ # ! 8% ,% ," ,# ( # ! - < 7 ( ,# %$ # ! 9 2

2 2 2 - -------------------- ---------------- -----------------------

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2

2

---------------- ------------ ----------------------- 2

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--- ---

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---

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

— 112 —

' " ' " ' " ' "

- 0 % ' 2 ('. - ) % ( , : $ % - '( % ' # < %$ ' V 9 %# 5% # : 7 2 I . F ' # %$ 2 I 5 ' # %$ ' 2 5 ', 5

#$

+, : " % # #$ %$ ' - 1 , %$ '

— 113 —

8% ,% ," ,# ( # ! - 7 ( ,# < %$ # ! 8% ,% ," ,# ( # ! - < 7 ( ,# %$ # ! 9 2

2 2 2 - -------------------- ---------------- -----------------------

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2

2

---------------- ------------ ----------------------- 2

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--- ---

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---

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

— 112 —

' " ' " ' " ' "

- 0 % ' 2 ('. - ) % ( , : $ % - '( % ' # < %$ ' V 9 %# 5% # : 7 2 I . F ' # %$ 2 I 5 ' # %$ ' 2 5 ', 5

#$

+, : " % # #$ %$ ' - 1 , %$ '

— 113 —

Ê ïàðàãðàôó 7

% - '(

---

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114

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115

Ê ïàðàãðàôó 7

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116

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Ê ïàðàãðàôó 8 ---

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117

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Ê ïàðàãðàôó 8 ---

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117

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à ë à â à IV

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§ 9. Ñóììà è ðàçíîñòü ìíîãî÷ëåíîâ 24. Ìíîãî÷ëåí è åãî ñòàíäàðòíûé âèä 0 ' # 5 % - ' 0 ' ( 5 % - ' ' - # 5 % - ' 0 ' ', # 5 % - ' %# '.5 ' '. ( 5 % - ' ' # 5 % - '

'. - # 5 % - '

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119

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à ë à â à IV

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118

§ 9. Ñóììà è ðàçíîñòü ìíîãî÷ëåíîâ 24. Ìíîãî÷ëåí è åãî ñòàíäàðòíûé âèä 0 ' # 5 % - ' 0 ' ( 5 % - ' ' - # 5 % - ' 0 ' ', # 5 % - ' %# '.5 ' '. ( 5 % - ' ' # 5 % - '

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25. Ñëîæåíèå è âû÷èòà íèå ìíîãî÷ëåíîâ

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25. Ñëîæåíèå è âû÷èòà íèå ìíîãî÷ëåíîâ

— 121 —

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§ 10. Ïðîèçâåäåíèå îäíî÷ëåíà è ìíîãî÷ëåíà

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26. Óìíîæåíèå îäíî÷ëåíà íà ìíîãî÷ëåí

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§ 10. Ïðîèçâåäåíèå îäíî÷ëåíà è ìíîãî÷ëåíà

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26. Óìíîæåíèå îäíî÷ëåíà íà ìíîãî÷ëåí

127

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— 128 —

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