ГДЗ - алгебра - 11 класс - Алимов

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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=