1

1 $1.1

-

1. * , .

2. * , .

3. * f, f(x)=

, .

4. * x2 + y2 = 1 x, y ( R, .

5. * g g (x) = x2 .

6. * f f (x) = 20x .

7. * h h (t) = (

, t ( R+, .

8. * f f (t) =

, t ( R+, .

9. * f, ( R, f (x) = f (y) x, y ( A, x = y.

10. * A f, g , S=f+g .

11. * A f, g , h=

.

12. * .

19. * f , x1, x2 ( x1 > x2 f (x1) < f (x2).

20. * f , x1, x2 ( x1 0, .

16. * f (x) =

, x < 0, .

17. * .

18. * f, , , .

11. * f x0 , . f (x0) = 0

. f (x0) ( 0 .

f (x) .

f(x)=f(x0) .

f(x)(f(x0)

12. * . x0 . 1

. 2 . 3 . 4 . 5

-

2. *

f (x) = - 2,

g (x), :) g (x) = 3 f (x) - 1

g (x) =) g (x) = 2 - 4 f (x)

g (x) =

) g (x) = (2 f (x))2

g (x) =) g (x) =

g (x) =

) g (x) =

g (x) =

3. * :)

(2x2 + 6x - 1) = )

= )

(5

) =

)

[(3x + 2) (5x - 3)]2 =

)

[x + 3x] = )

[2x - 4x] =

4. * :)

EMBED Equation.3 = )

EMBED Equation.3 =

)

EMBED Equation.3 = )

EMBED Equation.3 =

6. ** f, g f(x)=2x2-3x+1 , g(x)=5x2-1, x ( R. :)

f (x)

g (x)

)

[f (x) + 2g (x)]

7. ** (x) =

. : ) , )

(x))

[ (x)]38. ** f f (x) =

. : ) , )

f(x)

9. ** f, g f(x)=6x3+5x-1 , g(x)=2x-1, x ( R. :)

f (x),

g (x) )

10. **

f (x) = - 2,

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

) (x) =

11. ** f f (x) =

. : ) , )

f (x)

12. ** f f (x) =

. : ) , )

f(x)

13. ** f f (x) =

. : ) , )

f (x)

16. ** f f (x) =

. : ) )

f(x).) , f (x) x0 = 1.

17. ** f f(x)=

.) x ( 3 ; ) ( R f (x) x0 = 3; 18. ** f f(x)=

. :)

f (x) ) ( R, f x0 = 2.

19. ** f f(x)=

. : ) ,

)

EMBED Equation.3 ) ( R, f x0 = 1

20. ** f f(x)=

. (R, f x0 = 2.

1

-

-

21. * f (x0) f x0 .22. * f, (x0,f(x0)) , f x0. 23. * f x0 y = f (x), x, x = x0.24. * f (x0) f x0

EMBED Equation.3 h(R*25. * f x0 ,

EMBED Equation.3 h(R, h(0. 26. * f(x) =

x0=0. 27. * f(x)=

x0=0. 28. * f x0 ,

EMBED Equation.3 , h ( 0, , f (x0,f(x0)).29. * f(x)=

f(x)=

. 30. * g()=q, q(Q, g () = qq-1. 31. * f(x)=x g(x)=x f (x)=(x) = x g(x)=(x)=-x. 32. * (x)=ex L(x)=lnx (x)=(ex)=ex L(x)=(lnx) =

. 33. * g l, g g(x)=cx, c(R-{1}. 34. * g 4 , g 5 . 35. * g , g 2 . 36. * f f(x)=

EMBED Equation.3 , h(0, x f f , () f. 37. * ( ) g g. 38. * ( ) g g. 39. * f (x) = 5 f(x)= 5x. 40. * s(t)=t s(t)=1. 41. ** f f . 42. ** f x0 , f (x0), f (x0)=0. 43. ** f, , f (x0) f (x0) ( 0, x0 , x0 f. 44. ** f, . , f , 45. ** f, . x , f f (x) , .46. ** f x0 x0, f (x0, f (x0)) xx.

13. * f x0 , .

, h(R, h ( 0 .

EMBED Equation.3 , h(R*..

, h ( R, h(0 .

= + (, h ( R*, .

= - (, h ( R*

14. * f, x0 , . x0 .

, h(0 . f(x) x x=x0 . f (x) x - x0 .

15. * f (x0) f x0 .

, h ( R, h ( 0.

(

), h ( R, h(0.

, h ( R, h ( 0.

, h ( R, h ( 0.

, h ( R, h ( 0

16. * S (t) t, ,

, h ( R, h ( 0 . t=t0 B. [t0, t0 + h] . [t0, t0 + h] . t = t0 E. t0 t0 + h

17. * S (t) t, , =

EMBED Equation.3 , h ( R, h ( 0 . t= t0 B. [t0, t0 + h] . [t0, t0 + h]

. t = t0 E. t0 t0+h

18. ** f (R , f . B. .

. f E.

21. * H f, , , . f (x)=0, x

B. f (x) = 0, x . f (x) > 0, x . f (x) < 0, x E.

22. * f, , , . f(x)=0, x B. f (x) = 0, x . f (x) > 0, x .f(x) 0 f(x0)=0

24. * f(x)=x2 ( h( 0) .

EMBED Equation.3 B.

h(2x+h) .

EMBED Equation.3 . 2 E. x

25. * x, ( 0, ( 1, . B. . 2x-1 . x-1 E.

26. * h (x) =

. f (x)=

g(x)=xB. f(x)=x2 g(x)=

. f (x) = x

. f (x) =

E.

27. * f (x) = 3x . f (x) = 3x B. f (x) = 3x . f (x) = x, g(x)=3x. f(x)=

E.

28. * L (x) = f (g (x)), f, g , . L (x) = f (g (x)) B. L(x)=f(x) ( g (x) . L (x) = f (x) + g (x). L(x)=f(g(x))(f(x). L (x) = f (g (x)) ( g (x)

-

5. * :) f (x) = x2 f (0) = ) f(x)=x2+1 f (1)=..) f (x) = 2x2 3, f (-1) =.. ) f (x)=x, f(

)=.. ) f (x) =

, f (0) =

6. * :) f (x) = x2 - 1 A (0, f (0)) y =

) f (x) = 2x2 - 1 A (1, f (1)) y =

) f (x) = 3x2 - 2 A (- 1, f (- 1)) y =

7. * y = f (x) .

21. ** . , :)

)

22. ** , ( = 90() 12m2. x , y .

23. ** r 30cm2. ,

24. ** f f (x)=

, x ( R. : ) f (3) ) f, x=3 )

25. ** f f(x)=x2, x(R (R.) f (2). ) , f (2, f (2)) 4.

26. ** f f (x) = x2 + 1, x ( R. ) f (0). ) f x=0. ) f (0, f (0)).

27. ** f f (x) = x2 - 5x + 6, x(R. : ) f (x) ) f, xx.

28. ** f f (x) = 2x2 - x, x(R, (R. ) f(2). ) , f (2,f(2)) xx 45(.

29. ** xx , f(x)=-2x2+x-3 (

,f(

)).

30. ** , S(t)=2t+t2, t sec S . : ) [0, 4] sec ) , t = 1 sec (1 sec ).

31. ** , , t ( sec) S(t)=3t2-t. : ) [2, 4] sec ) , t = 3 sec (3 sec ).

32. ** , , , t ( sec), (t)=3t2 - 5. ) () t, t=t0. ) () t, t = 10 sec (10 sec ).

33. ** t ( ) (t)=103-5(102 (1 + t)-1. ) (t=0). ) t=9 . ) , t = 9 . 34. ** , t ( ) (t) = 10 ( e0(04t ( ). , , 25 .

35. ** f, g f (x) =

, g(x)=ex(x2. : ) i) f ii) g. ) i) f(1) ii) g(1).

36. ** (x) , (0) = - 1, (1) = 5, (0) = 2, (1) = 2.

37. ** f f (x) = 2x - x2. ) : i) f (x)ii) f (x) ) : (1 - x) f (x) + f (x) = 0, x ( R.

38. ** f f (x) = e2x. ) : i) f (x)ii) f (x)) : 2f(x) - f (x) = 0, x(R.

39. ** f f (x) = ex, ( R. : ) f (x) ) f (x) ) , f(x)+2f(x)=3f (x), x ( R.

40. ** f f(x)=(3x-2)(

. : ) f (x) ) f (0).

41. ** f f (x) =

. : ) , ) f (x).

42. ** f f (x) =

. : ) , ) f (x).

43. ** f f (x) =

. : ) , ) f (x).

44. ** f f (x) =

x3+2x2+3x+1, x(R. : ) f (x) ) , , xx.

45. ** f f (x) = (x + 1)2, x ( R. : ) f(x) ) f 4.

46. ** f f (x)=-x2+3x-1, x ( R. : ) f(x) ) f, xx 135(.

47. ** f f (x)=(x + 1)2, x(R, (R. ) f (x). ) , f (1, f (1)) 4. ) .

48. ** f f (x) = x2 - 4x + 2, x(R. ) f (x) ) f, 45( xx.

49. ** f f (x) = 2x2 - x +, , ( R y = 3x - 1, x ( R. , y = 3x - 1 f 2.

50. ** f f(x) =

x3+x2-2x+1, x(R. : ) f (x).

) f, y=x+3.

51. ** f f(x)=

, x(R, x(0. ) f () =-

( R, (0. ) (,

) f.

52. ** f f(x)=x3-9x2+15x-3, x(R. ) f (x). ) . ) ( ).

53. ** f, g : f(x)=2x2-4x-1 g (x) = 4x - x2 + 2, x ( R. : ) i) f(x) ii) g (x). ) ) .

54. ** f f(x)=

x3-2x2-5x-2, x(R. : ) f(x) ) x f(x)=0 ) x f ) .

55. ** f f (x)=x2+x+3, x(R, ,(R. ) , f x = 1 - 2. ) x = 1;

56. ** f f (x) = x3 - 3x, x ( R. f : ) )

57. ** f f (x) = x2(e-x. ) f (x), f (x). ) f, . ) ( ).

58. ** f f(x)=(2x - x2) ex, x(R. ) : i) , ii) f(x) f(x). ) f : i) , ii) , .

59. ** f f (x) = x3 + x2 + 3x - 1, x(R, , ( R. ) f (x). ) , , f x1=2, x2=-2.) .

60. ** , ;

61. ** 1600 m2, , .

62. ** , R, .

63. ** x, y 12, .

64. ** 1.000 . ( ) : (t)=t2+250t-1 ) ; ) ;

65. ** , : ()=

[2(-35)2+750] ) ; ) ;

66. ** W (t), , t : W (t) = 6t2 - t4 Joules. ) ( ) t=t0. ) ; ) Joules ;

67. ** 8 100 . 8 : (t)=t2+

t((0,8] . ) . ) ;

68. ** () f(x)=x2(-x), >0 x mg. ;

69. ** . x (

+25x+ 25) . (1000 -

) ., , ;

08.02

1211

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