Final_Mat_Anal
.docВопрос № 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 = x3/2.
Вопрос № 98
$$1 Gini index is coefficient of equality, it is defined by integral:
Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y = x5/2.
Вопрос № 99
$$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 = x7/3.
Вопрос № 100
$$1 Gini index is coefficient of equality, it is defined by integral:
Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y = x5/3.
Вопрос № 101
$$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 : un ≤ vn , then
a) from convergence of follows the convergence of .
b) from divergence of follows the divergence of .
The test is known as:
Вопрос № 122
$$1 Let for ( un ≥0) the limit exist: , then
a) the series converges if ;
b) the series diverges if ;
c) the test fails if .
Вопрос № 123
$$1 Let for ( un ≥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
$$1 Let un=f(n) (f(x) and positive). Then the and the integral both are convergent or divergent.
The test is known as:
Вопрос № 125
$$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)