# гдз по алгебре 11 класс алимов ш. а. и др

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• 11

10-11

10-11 .. .,-.: , 2001.

• 4

VIII . 44 .................................................................................... 4 45 .................................................. 6 46 ...................................................... 10 47 .................... 20 48 .......................................... 29IX . 49 .............................................. 45 50 .................................................................. 49 51 ........................................................ 54 52 ........................... 70 53 , ........................ 78 IX. .................................................................... 80X . 54 .............................................................................. 96 57 ............................................................. 107 58 ........................ 110 59 ......................................................... 123 ..................................................................... 124 . ............................................................... 134

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• 5VIII .

44 776.

s(t)=1+3t; vcp= h)t(s)ht(s + . T.k. s(t)=1+3t, s(t+h)st=

=1+3(t+h) (1+3t)=1+3t+3h13t=3h, vcp= hh3 =3.

, :

1) h=41=3, s(t+h)=1+34=13, s(t)=1+31=4, vcp= 3413 =3;

2) h=10,8=0,2, s(t+h)=1+31=4, s(t)=1+30,8=3,4,vcp= 2,0

6,02,0

4,34 = =3.

777.1) s(t)=2t; vcp= h

h2h

t2)ht(2h

)t(s)ht(s =+=+ =2: h=1,21=0,2

s(t+h)=21,2=2,4; s(t)=21=2; vcp= 2,04,0

2,024,2 = =2

2) s(t)=t2 t=1; (t+h)=1,2;

vcp= =++=+=+ hthth2t

ht)ht(

h)t(s)ht(s 22222

=2t+h=21+(1,21)=2,2. 778.1) s(t)=2t+1;

) s(t+h)s(t)=2(t+h)+12t1=2t+2h+12t1=2h;

) vcp= hh2

h)t(s)ht(s =+ =2; ) 2limvlim

0hcp

0h = =2;2) s(t)=23t;) s(t+h)s(t)=23(t+h)2+3t=23t3h2+3t= 3h;

) vcp= hh3

h)t(s)ht(s =+ = 3; ) )3(limvlim

0hcp

0h= = 3.

779.s(t)=0,25t+21) h=84=4;

vcp=( )

42122

42425,024425,0)()( +=++=+

htshts =0,25

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• 62) v(t)= 25,0limvlim0h

cp0h = =0,25.

780.1) f(x)=3x+2;) f=f(x+h)f(x)=3(x+h)+23x2=3x+3h+23x2=3h;

) hh

hf 3= =3; )

hflim

0h

=3, .. f (x)=32) f(x)=5x+7;) f=f(x+h)f(x)=5(x+h)+75x7=5x+5h+75x7=5h;)

hh5

hf = =5; ) 5lim

hflim

0h0h = =5;

3) f(x)=3x25x;) f= f(x+h)f(x)=3(x+h)25(x+h)3x2+5x==3x2+6xh+3h25x5h3x2+5x2=6xh+3h25h;

) =hf =+

hhhxh 536 2 6x+3h5; )

0h0hlim

hflim =

(6x+3h5)=6x5;4) f(x)= 3x2+2;) f= 3(x+h)2+2+3x22= 3x26xh3h2+2+3x22= 6xh3h2;) =

hf =

hhxh 236 6x3h; )

0h0hlim

hflim

= (6x3h)= 6x.

781.1) f (x)=4; 2) f (x)= 7; 3) f (x)= 5. ( ).

782.1) s(t)=

23 t2;

) s(t+h)s(t)=23 (t+h)2

23 t2=

23 t2+3th+

23 h2

23 t2=3th+

23 h2;

) vcp= =+=+ hhth3

h)t(s)ht(s 22

33t+

23 h;

) v(t)= 0h

cp0h

limvlim = (3t+ 23 h)=3t;

2) s(t)=5t2;) s(t+h)s(t)=5(t+h)25t2=5t2+10th+5h25t2=10 t h +5h2;

) vc p= =+=+ hh5th10

h)t(s)ht(s 2 10t+5h;

) v(t)= 0h

cp0h

limvlim = (10t+5h)=10t;

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• 7 783.s(t)=t2+2 v (t):) s(t+h)s(t)=(t+h)2+2t22=t2+2th+h2+2t22=2th+h2

) vc p= =+=+ hhth2

h)t(s)ht(s 2 2t+h

) v(t)= 0h

p c0h

limvlim = vc p= 0hlim 2t+h=2t1) t=5, v(5)=25=10; 2) t=10, v(10)=210=20.

784.1) [0; 1] vc p= 5,11

05,1)()( ==+h

tshts ;

2) [1; 2] vc p= ==+ 15,15,2

h)t(s)ht(s 1;

3) [2; 3] vc p= 5,015,23)()( ==+

htshts .

785.1) [0; 2] vc p= 2

10221

h)t(s)ht(s =

=+ ;

2) [2; 3] vc p= 2313

=2; 3) [3; 3,5] vc p= 35,3

34 =2.

786.1)

1limx (2x+1)=3, .. f(x)=2x+1, :

|f(x)3|=|2x2|=2|x1|

• 8 789.

1) x

xxx2

121

21 2

1121

21

===

; 3) 7

972

72 =

xx ;

2) 32

31

31 =

xx ; 4) 133 3 =

xx .

( ). 790.

1) ( ) 6655 551 xxxx ===

; 2 ) ( ) 101099 991 xxxx ===

;

3) ( )4 3

43

41

4

4

141

xxxx ==

= ;

4) 331

32

3 2

32

32

xxxx ==

=

;

5) 3311

'

31'

3 31

311

xxxx

x==

=

;

6) 4 2

431

'

43'

4 3 4

3431

xxxx

x==

=

.

( ). 791.

1) ((4x3)2)=2(4x3)4=8(4x3);2) ((5x+2)3)= 3(5x+2)45= 15(5x+2)4;3) ((12x)6)= 6(12x)7(2)=12(12x)7;4) ((25x)4)=4(25x)3(5)= 20(25x)3;5) ((2x)3)=3(2x)22=6(2x)2=24x2;6) ((5x)4)=4(5x)3(5)= 20(5x)3=2500x3;

792.1) ( ) ( )

3 232

313

)7x2(3

22)7x2(317x27x2

+=+=

+=+ ;

2) ( ) ( )4 3

43

414

)x37(4

3)3()x37(41x37x37

==

= ;

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• 93) ( ) ( )4 3

43

414

274

33)3(4133

xxxx ==

= ;

4) ( ) ( )3 2

3

3 232

313

3

5

253

55)5(3155

xxxxx ===

= ;

793.1) f (x)=(x6)=6x5; f (x0)=6 16

3326

21 5 ==

2) f (x)=(x2)= 2x3= 32

xf (x0)= 27

2323 =

3) f (x)= ( )x

xxx2

121 2

121

==

= f (x0)= 4

142

1 =

4) f (x)= ( )3 2

32

31

3

3

131

xxxx ==

= f (x0)= 12

1

83

13 2

=

5) f (x)= ( )x

xxx45

2)4()45(21)45((45 2

121

===

f (x0)= 2145

2 =

6) f (x)= ( ) ( )323

21

132

33)13(2113

131

+=+=

+=

+

xxx

x

f (x0)= ( ) 163

1132

33

=+

.

794.

y = 4x3

y = x4

795.1) =(x2)=2x, y(0)=20=0, y(1)=21=2, y(1)=2(1)= 2

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• 10

2) =(x3)=3x2, y(0)=30=0, y(1)=31=3, y(1)=3(1)2=3

3) =x

x2

121

=

y(0) , .

796.

1) ( ) =

+ 2321

x ((2+3x)2)= 2(2+3x)33= ( )332

6x+

2) ( ) =

3231

x((32x)3)= 3(32x)4(2)= ( )423

6x .

3) ( ) ( ) ( ) 331323 2 232323

322323 ==

=

x

xxx .

4) ( ) ( ) ( ) ( )7 5)75

727 2

x143

414(x14372x143x143

==

=

.

5) ( ) ( ) ( )3 431

37x3

137x3317x3

7x31

34

==

=

.

6) ( ) ( ) ( ) ( ) ( )3 532

3 2 x213

42x2132x21

x21

135

==

=

.

797.1) f(x)=x3, f (x)=3x2, f (x)=1 3x2=1; x=

31 ;

2) f(x)= 3 2x , f (x)= 332

32

31

32

xxx ==

, f (x)=1 332

x=1,

278= x

323 =x .

798.s(t)= 1t + ; v(t)=(s(t)) =( 1t + ) = ( ) ( )

1t211t

211t 2

121

+=+=

+ ;

v(3)= 41

1321 =+ .

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• 11

799.1) f(x)=(2x1)2; 2) f(x)=(3x+2)3;f (x)=2(2x1)2=4(2x1); f (x)=3(3x+2)23=9(3x+2)2;f(x)=f (x) (2x1)2=4(2x1); f(x)=f (x) (3x+2)3=9(3x+2)2;(2x1)(2x14)=0; (3x+2)2(3x+29)=0;(2x1)(2x5)=0; (3x+2)2(3x7)=0;

( )

==

052012

xx

2521

==

x

x;

===+

0073023

xx

37

32

==

x

x;

2x1=0 x=21 ; 3x+2=0 x=

32 ;

(2x5)=0 x=25 ; 3x7=0 x=

37 .

800.) , , , y=ax2+bx+c a>0, .. .

a2

bxb = , x b=0 b=0 y=ax2+c. :1=(0)2+ c=1 y=ax2+1;2=a(1)2+1 a=1 y=x2+1;) , , y=ax2+by+c.. . , a

• 12

46 802.

1) (x2+x)=2x+1; 5) (4x3)= 43x2= 12x2;2) (x2x)=2x1; 6) (0,5x3)=1,5x2;3) (3x2)=32x=6x; 7) (13x2+26)=26x;4) (17x2)= 172x= 34x; 8) (8x216)=16x.

803.1) (3x25x+5)= 6x5; 5) (x3+5x)=3x2+5;2) (5x2+6x7)= 10x+6; 6) (2x3+18x)= 6x2+18;3) (x4+2x2)=4x3+4x; 7) (2x33x2+6x+1)=6x26x+6;4) (x53x2)=5x46x; 8) (3x3+2x2x5)= 9x2+4x1.

804.y=3(x2)2+1=3x212x+12+1=3x212x+13;y=6x12.

805.1) 43

2 321x

xx

x =

+ ; 2) 3223231x

xx

x =

+ ;

3) ( )xx

xxxx2

1

2

121

4122

4 34 2

143 == ;

4) ( )14 136 5

146

2

1

2

11417

61373 14

1365

xxxxxx +=+= .

806.1) f (x)=(x22x+1)=2x2; f (0)=202= 2; f (2)=222=2;2) f (x)=(x32x)=3x22; f (0)=3(0)22= 2; f (2)=3222=122=10;3) f (x)=(x3+x2)= 3x2+2x; f (0)=30+20=0; f (2)= 322+22=2+4=8;4) f (x)=(x2+x+1)=2x+1; f (0)=20+1=1; f (2)=22+1=5.

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• 13

807.1) f (x)=

=

+ 322

2111xxxx

;

f (3)=275

32

31

33 =

; f (1)= 12= 3;

2) f (x)= 21

2111

xxxx =

++ ;

f (3)=91

321 ; f (1)=

21 1=

21 ;

3) f (x)= ( )

+=

=

43

43

6

2

33221323 2

3

xxxx

xx

f (3)= ( )296

231 f ;

272

321

272

3233 =+=+=+ ;

4) f (x)=

+=

=

223

23

23

23

25

21

23

23

xxxxxxx ;

f (3)=9

31433

1436

2836127

3183

233 ===+=+ ; f (1)=

23

23 + =3.

808.1) , .. =1 =

12x

2) , .. =3 = ( )2353

xx

3) ( ) ( )12

11211 2

1

+=+=+=

xxxy ,

(0)= 21

1021 =+ ;

4) ( ) ( ) ( ) xxxy === 5 115215 21 , (4)=

451 = 1 .

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• 14

809.1) f(x)=(x32x)=3x22 f (x)=0; 3x22=0; x2=