1. II. .
  2. II. Ͳ
  3. IV. .
  4. Quot; " . . . -.
  5. .
  6. . . . "" . . .
  7. . . . "" . . " ".

, g, f. g (531-532).

531. a) f {x) = 2x-f-l; 6) f (x) = - ^ - x -1;

j

532. a) / (*) = - j-; 6) f (x) = 2x2(X ^ 0) \

B> ^^=I + 2 ;/ W = V ^ + 1 *

533. , /:

) / () = 2 *3+1; ) / (*) = (: +1)2, * 6 (-; -1];

)f (x) = -2 *3+1; )f (x) = (x-I)2, * ? [1; ).

534. / (. 141) f g -2, 1 3. g, :

) / (*) = / iW; ) f (x) = f2(X) ',) f (x) = f3(X);) f (x) = f4(X).


, f

. , f (535-536).

535. a)f (x) = x2- \ -1, ) /() = 2,(- ; );

) / (*) = V *. * 0; )} () = ? +1, (-; ).

536. a) f (x) = smx, * [-? ; --]; ) f (*) = tg > * (--fs --); ) f () = cosx, 6 [0; ]; ) f () = ctgx, * 6 (0; ).

11. ղ ֲ

41.

1. . ( ), . - , .

= , 2; 2,3; 3; 3,4 (. 142), 0. 35, 40, 48 51 , . . dz = (0; 1) tg 35 tg 51 . , , 2 3, , 1 (. . 45 ). ( ):

, 2 3 ( ), = 0 , 1, . .

___.

- * -> 0. (1)

. , . . : - +2,718281828459045 ....

.


. 142

2. .

1. ,

( = .

. = :

= + - * = - - = (& - 1).

(1), :


: - * 0.

_ (* - _

, '= *, . . (I = - .

1. = 5:

(5 = 5- (5) '= 55.

1, .

. ( In) :

In = log, . (2)

- 1= . *

= (1)= 1.(3)

.

2. ,

( = In .(4)

. (3) ,

( *) ' = (1 = 1 \ = \ .(5)

.  , . . - * ~ -

(. . 111).

2. = 2 * = 5 ~3. (4) (2) '= 2 * In 2; (5 "3*) '= (-) * 5 "3:In 5. 3. f (x) = xex () .

:

/ '(*) = ( = '+ : () '= + (1 + ).

> 0 - :, / ' (l-f-x). , / '(*)> 0 (-1; ), f [- 1; ). (- ; - 1) / '(*) <0, f (-; -1]. = - I , , , = - 1 .

143.

3. .

3. R

X

.

ij, In - ,

(I ? r) '= T ^ rW =

= -J-In =

In

- . ,


if - R. (),= , R. 4. : ) / (*) = 5 '; ) g (x) = 4-2 "; ) h \ x) = 4eZx- 10-0,6. 3 , :

5. , = 3, = 0, * = -1, = 2. (. 144). S :

. 144

a) f (x) = e , 0= 0; ) f (x) = ex, 0= 0;

) f (x) = 3x, 0= 1;

) / (*) = 2 ~, 0= 1.


541. :

) / (*) = 5 ; ) f (x) = 2-3'-, ) / (*) = ; ) f () = - - '+ 1.

542. :

1112 a) J 0,5Xdx; ) \ e2xdx \ ) \ 2Xdx \ ) \ 3Xdx.

- 2JL

(543-544).

X

543. ) = >sin ) = 72tg3x;

) = ^ cos 2 :; ) / = 2 "ctg

544. ) = --) = - ^ \

3v 0,3 " '

) = ^ \)

3-

2+ 5 7* V ^ + 0,5 '

545. () :

) f (x) = xe5x; ) / () = ? 2 ~;) f () = ~\) f () = 40,5.

546. :

a) f (x) = e3~2x\) / ( :) = 2-0,9X-5,6 "*; ) } () = 2 '0-) /() = 3+ 2,31 + .

, (547-548).

547. ) = , =0, = 0, = \;) = 3, = 9, = 1; ) = 2, =0, = -1, = 2 \) = , = 2, = \.

548. a) =3, = \\) y = exty = e ~xt = \ ) = (^ -)'= ' = -2 \) = (- ^ -) . = 4, =4.

42.

, . = logo * = = . - , , . - . .


, -

= 1 , . . ( /? +). 1, . .

^ = (1) '. (2)

³, '= \.

1 (. 41): (1) '= 1In7 = In '. ϳ (2), 1 = In ', \ ' = - ^ ~.

1. : ) = \ (5 +2 );

) = log3*; ) = log72 *.

) (ln (5 + 2 *) y =Tl5r. (5 + 2 *) '= -gJ5-;

) (1 *) '= (- ? )' = ^ -;

) (\ Og12Xy = (y- ^ -) '= - ^T= ^pr.

2. f () = 2In , , .

> 0. :

f () = 2 In - 2- ^ - = 2 In - \ - = 2 (^ \ * + - ? -) - > 0, ^ In * + ? ").

, / '()> 0 (; ),

'' V

-; ) ; L- / '

(; -) , f -

V - '

(0; -1. -

V - / J [

, , ; f (^ =) = ~

145.

(1) , -

(0; ) - In + .

-j- (-; 0), 1 (- ). ,

(In 1) = - 7 '

1 : | = : > 0 | : | = - , , - , 0, - In \ \.

3. -

X

In | + 3 | + ( - , -3). In | 5: + 714-



LogsV5 1 | . , f {) -, ( ).

, 0 < | - | <6 . | . F f , | (x) - F (x) -fC. | , / () - F () -, . | . - ' , - . | ) W61,7; ) (i-) 3 . | | . b , , . | Log & X | \ lg 8-j-lg 18 log3 16. |

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