VI. Контрольные вопросы.

№ варианта

Функция

y = f (x)

Отр-к

инт-ния

[a, b]

Точное значение

m = min f(x)[a, b]

M = max f(x)[a, b]

1

2

3

4

5

1

y = (x-3)²*e^|x|

[-1, 4]

2

y = (x-3)³*e^|x+1|

[-2, 4]

3

y = e

[-2, 1]

4

Y = ln(1+ )

[-2, 1]

5

Y = arcctg

[-1, 2]

6

Y =

[-1, 2]

7

y = arcctg

[-1, 2]

8

y = cos(x + signx) + sin(x+π/6)

[-π, π]

9

y= sin(x-π/4) - cos(x - signx)

[-π, π]

10

y = sin(x- ) - cos(x- signx)

[-π, π]

11

y = 2arcctgx + arcsin(2x/(x² + 1)

[-π, π]

12

y = 4x + (9π²)/x + sinx

[π, 2π]

13

y = cos²x + cos²(π/3 + x) -cosx*cos(π/3+x)

[- π, π]

14

y = 2Sinx + Sin2x

[0, 3/2π]

15

y = x - 2lnx

[3/2, e]

16

y =

[-2, 1]

17

y=

[-1, 1]

18

y =

[0, 1]

19

y = x⁵ - 5x⁴ + 5x³ + 1

[-1, 2]

20

y = x - 2

[0, 5]

21

y = 0,625x⁴ + 0,5x² - 1,2502x

[0, 3]

22

y = 0,5x² + x + -2,5x

[0, 3]

23

y = 0,0393x³ - x²lnx + 0,25x²

[1, 2]

24

y = 1,5x² - 4xlnx + 4x

[2, 4]

25

y = e^x + e^-x - 2x

[0, 1]

26

y = 1,5x² - 14x + e^x + e^-x

[1, 3]

27

y = 2x - 0,5x² – Cosx -(1+x)ln(1+x)

[0, 3]

28

y = -

[-2, 1]

29

Y = xlnx – ½*x² + 0,8x

[-0,5, 3]

30

y = 1/3*x³ - (1+x)ln(1+x) + x -2

[-0,5, 3]

31

y = x/lnx

[-1, 1]

32

y = 2x² - lnx

[-1, e]

33

y = x - 2sinx

[0, 2π]

34

y = 2sinx + cos2x

[0, 2 π]

35

y = x

[0, 2]

36

y = 2x³ - 3x³

[-1, 1]

37

y = x⁴ - 2x² + 5

[-2, 2]

38

y = x + 2

[0, 4]

39

y = x⁵ - 5x² + 5x³ + 1

[-1, 2]

40

y = x³ - 3x² + 6x - 2

[-1, 1]

41

y =

[-6, 8]

42

y = (1 – x + x²)/(1 + x - x²)

[0, 1]

43

y = (x - 1)/(x + 1)

[0, 4]

44

y = 1/x + 1/(1 - x)

[0, 1]

45

y = sin2x - x

[-π/2, π/2]

46

y = 2tgx – tg²x

[0, π/2]

47

y = x⁴

[0,1, +∞]

48

y =

[0, 3]

49

y = arctg

[0, 1]

50

y = x*sinx + cosx – (¼)*x²

[-π/2, π/2]