Final_Mat_Anal

Вопрос № 1

$$1 Determine the domain of the function:

Вопрос № 2

$$1 Determine the domain of the function:

Вопрос № 3

$$1 Determine the domain of the function:

Вопрос № 4

$$1 Determine the domain of the function:

Вопрос № 5

$$1 Determine the domain of the function:

Вопрос № 6

$$1 Find the limit of the function:

Вопрос № 7

$$1 Find the limit of the function:

Вопрос № 8

$$1 Find the limit of the function:

Вопрос № 9

$$1 Find the limit of the function:

Вопрос № 10

$$1 Find the limit of the function:

Вопрос № 11

$$1 Find the limit of the function:

Вопрос № 12

$$1 Find the limit of the function:

Вопрос № 13

$$1 Find the limit of the function:

Вопрос № 14

$$1 Find the limit of the function:

Вопрос № 15

$$1 Derivative of multiplication is

Вопрос № 16

$$1 Derivative of division is

Вопрос № 17

$$1 Take derivative of the function:

Вопрос № 18

$$1 Take derivative of the function:

Вопрос № 19

$$1 Take derivative of the function:

Вопрос № 20

$$1 Take derivative of the function:

Вопрос № 21

$$1 Take derivative of the function:

Вопрос № 22

$$1 Take second order derivative of the function:

Вопрос № 23

$$1 Take second order derivative of the function: y = sin(x²+7)

Вопрос № 24

$$1 Take derivative of the function: y = (ln(x))³

Вопрос № 25

$$1 Take derivative of the function: y = (lnx)²

Вопрос № 26

$$1 Take derivative of the function: y =

Вопрос № 27

$$1 Take derivative of the function: y =

Вопрос № 28

$$1 Take derivative of the function: y = tan().

Вопрос № 29

$$1 Take derivative of the function: y = cos()

Вопрос № 30

$$1 Take derivative of the function: y = cot()

Вопрос № 31

$$1 Find the interval where the function is increasing:

Вопрос № 32

$$1 Find the interval where the function is decreasing:

Вопрос № 33

$$1 Find the extreme points of the function :

Вопрос № 34

$$1 Find the extreme points of the function :

Вопрос № 35

$$1 Find the extreme points of the function :

Вопрос № 36

$$1 Find the interval where the function is concave up:

Вопрос № 37

$$1 Find the interval where the function is concave down:

Вопрос № 38

$$1 Find the points of inflection of the function:

Вопрос № 39

$$1 Find the interval where the function is concave up:

Вопрос № 40

$$1 Find the interval where the function is concave down:

Вопрос № 41

$$1 Find the points of inflection of the function:

Вопрос № 42

$$1 Find the equations of the vertical asymptotes of the function:

Вопрос № 43

$$1 Find the equations of the vertical asymptotes of the function:

Вопрос № 44

$$1 Find the equations of the horizontal asymptotes of the function:

Вопрос № 45

$$1 Find the equations of the horizontal asymptotes of the function:

Вопрос № 46

$$1 Find the partial derivative of the function of two variables:

Вопрос № 47

$$1 Find the partial derivative of the function of two variables:

Вопрос № 48

$$1 $$1 Find the partial derivative of the function of two variables: + xy

Вопрос № 49

$$1 Find the partial derivative of the function of two variables:-x³y

Вопрос № 50

$$1 $$1 Find the partial derivative of the function of two variables:

Вопрос № 51

$$1 Find the partial derivative of the function of two variables:

Вопрос № 52

$$1 Find the partial derivative of the function of two variables: -xy

Вопрос № 53

$$1 Find the partial derivative of the function of two variables: +xy

Вопрос № 54

$$1 Find the partial derivative of the function of two variables:

Вопрос № 55

$$1 Find the partial derivative of the function of two variables:

Вопрос № 56

$$1 Find the partial derivative of the function of two variables:

Вопрос № 57

$$1 Find the partial derivative of the function of two variables:

Вопрос № 58

$$1 $$1 Find the partial derivative of the function of two variables:

Вопрос № 59

$$1 Find the partial derivative of the function of two variables:

Вопрос № 60

$$1 Evaluate the indefinite integral:

Вопрос № 61

$$1 Evaluate the indefinite integral:

Вопрос № 62

$$1 Evaluate the indefinite integral:

Вопрос № 63

$$1 Evaluate the indefinite integral:

Вопрос № 64

$$1 Evaluate the indefinite integral:

Вопрос № 65

$$1 Evaluate the indefinite integral:

Вопрос № 66

$$1 Evaluate the indefinite integral:

Вопрос № 67

$$1 Evaluate the indefinite integral:

Вопрос № 68

$$1 Evaluate the indefinite integral:

Вопрос № 69

$$1 Evaluate the indefinite integral:

Вопрос № 70

$$1 Evaluate the indefinite integral:

Вопрос № 71

$$1 Evaluate the indefinite integral:

Вопрос № 72

$$1 Formula of Integration by parts is:

Вопрос № 73

$$1 What property of indefinite integrals is wrong:

Вопрос № 74

$$1 What property of indefinite integrals is wrong:

Вопрос № 75

$$1 Evaluate definite integral:

Вопрос № 76

$$1 Evaluate definite integral:

Вопрос № 77

$$1 Evaluate definite integral:

Вопрос № 78

$$1 Evaluate definite integral:

Вопрос № 79

$$1 Evaluate definite integral:

Вопрос № 80

$$1 Formula for area S enclosed between two curves y=f(x)

and y=g(x) determinates by formula:

Вопрос № 81

$$1 Formula that makes connection between definite and indefinite integrals is (Fundamental theorem):

Вопрос № 82

$$1 Find the area bounded between two curves:

Вопрос № 83

$$1 Find the area bounded between two curves:

Вопрос № 84

$$1 Find the area bounded between two curves:

Вопрос № 85

$$1 Find the area bounded between two curves:

Вопрос № 86

$$1 Find the area bounded between two curves:

Вопрос № 87

$$1 Find the area bounded between two curves:

Вопрос № 88

$$1 Find the area bounded between two curves:

Вопрос № 89

$$1 Find the area bounded between two curves:

Вопрос № 90

$$1 Find the area bounded between two curves:

Вопрос № 91

$$1 Average value over interval (a; b) of continuous function is defined by integral: .

Find the average cost of the function: C(x) = if x –output is changed: .

Вопрос № 92

$$1Average value over interval (a; b) of continuous function is defined by integral: .

Find the average cost of the function: C(x) = if x –output is changed: .

Вопрос № 93

$$1 Average value over interval (a; b) of continuous function is defined by integral: .

Find the average cost of the function: C(x) = if x –output is changed: .

Вопрос № 94

$$1Average value over interval (a; b) of continuous function is defined by integral: .

Find the average demand of the function: D(x) = if x –output is changed: .

Вопрос № 95

$$1 Average value over interval (a; b) of continuous function is defined by integral: .

Find the average demand of the function: D(x) =12-2x² if x –output is changed: .

Вопрос № 96

$$1 Gini index is coefficient of equality, it is defined by integral:

Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y =

Вопрос № 97

$$1 Gini index is coefficient of equality, it is defined by integral:

Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y = x^3/2.

Вопрос № 98

$$1 Gini index is coefficient of equality, it is defined by integral:

Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y = x^5/2.

Вопрос № 99

$$1 Gini index is coefficient of equality, it is defined by integral:

Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y = x^7/3.

Вопрос № 100

$$1 Gini index is coefficient of equality, it is defined by integral:

Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y = x^5/3.

Вопрос № 101

$$1 Find the general solution of differential equation:

Вопрос № 102

$$1 Find the general solution of differential equation:

Вопрос № 103

$$1 Find the general solution of differential equation:

Вопрос № 104

$$1 Find the general solution of differential equation:

Вопрос № 105

$$1 Find the general solution of differential equation:

Вопрос № 106

$$1 Find the general solution of differential equation:

Вопрос № 107

$$1 Find the general solution of differential equation:

Вопрос № 108

$$1 Find the general solution of differential equation:

Вопрос № 109

$$1 Find the general solution of differential equation:

Вопрос № 110

$$1 Find the general solution of differential equation:

Вопрос № 111

$$1 Find the general solution of differential equation:

Вопрос № 112

$$1 Find the general solution of differential equation:

Вопрос № 113

$$1 Find the general solution of differential equation:

Вопрос № 114

$$1 Find the general solution of differential equation:

Вопрос № 115

$$1 Find the general solution of differential equation:

Вопрос № 116

$$1 Find the common term of the number series:

Вопрос № 117

$$1 Find the common term of the number series:

Вопрос № 118

$$1 Find the common term of the number series:

Вопрос № 119

$$1 Find the common term of the number series:

Вопрос № 120

$$1 Find the common term of the number series:

Вопрос № 121

$$1 Let given two series: and

If for any n : u_n ≤ v_n , then

a) from convergence of follows the convergence of .

b) from divergence of follows the divergence of .

The test is known as:

Вопрос № 122

$$1 Let for ( u_n ≥0) the limit exist: , then

a) the series converges if ;

b) the series diverges if ;

c) the test fails if .

Вопрос № 123

$$1 Let for ( u_n ≥0) the limit exist: , then

a) the series converges if ;

b) the series diverges if ;

c) the test fails if .

The test is known as:

Вопрос № 124

$$1 Let u_n=f(n) (f(x) and positive). Then the and the integral both are convergent or divergent.

The test is known as:

Вопрос № 125

$$1 What series among harmonic series is/are convergent:

a); b) ; c) ; d) ; e)

Вопрос № 126

$$1 What series among harmonic series is/are divergent:

a); b) ; c) ; d) ; e)

Вопрос № 127

$$1 What series among following series is/are convergent:

a); b) ; c) ; d) ; e)

Вопрос № 128

$$1 What series among following series is/are divergent:

a); b) ; c) ; d) ; e)

Вопрос № 129

$$1Determine the interval of convergence with radius of the following power series:

Вопрос № 130

$$1Determine the interval of convergence with radius of the following power series:

Вопрос № 131

$$1Determine the interval of convergence with radius of the following power series:

Вопрос № 132

$$1Determine the interval of convergence with radius of the following power series:

Вопрос № 133

$$1Determine the interval of convergence with radius of the following power series:

Вопрос № 134

$$1Determine the interval of convergence with radius of the following power series:

Вопрос № 135

$$1Determine the interval of convergence with radius of the following power series:

Вопрос № 136

$$1 Find general solution of differential equation:

Вопрос № 137

$$1 Find general solution of differential equation:

Вопрос № 138

$$1 Find general solution of differential equation:

Вопрос № 139

$$1 Find general solution of differential equation:

Вопрос № 140

$$1 Find general solution of differential equation:

Вопрос № 141

$$1 Find general solution of differential equation:

Вопрос № 142

$$1 Find general solution of differential equation:

Вопрос № 143

$$1 Find general solution of differential equation:

Вопрос № 144

$$1 Find general solution of differential equation:

Вопрос № 145

$$1 Find general solution of differential equation:

Вопрос № 146

Вопрос № 146

$$1What series among following alternating series is/are divergent:

a); b) ; c) ; d) ; e)

Вопрос № 142

$$1What series among following alternating series is/are convergent absolutely:

a); b) ; c) ; d) ; e)

Вопрос № 143

$$1What series among following alternating series is/are convergent conditionally:

a); b) ; c) ; d) ; e)

Вопрос № 144

$$1What series among following alternating series is/are convergent conditionally:

a); b) ; c) ; d) ; e)

Вопрос № 145

$$1What series among following alternating series is/are convergent absolutely:

a); b) ; c) ; d) ; e)