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*-infinitvie
Вопрос № 1
$$1 Determine the domain of the function:
(-*; -5) U [3; +*)
Вопрос № 2
$$1 Determine the domain of the function:
x>3
Вопрос № 3
$$1 Determine the domain of the function:
x>6
Вопрос № 4
$$1 Determine the domain of the function:
x>=4
Вопрос № 5
$$1 Determine the domain of the function:
X=R-(nk)
Вопрос № 6
$$1 Find the limit of the function:
4/7
Вопрос № 7
$$1 Find the limit of the function:
0.3
Вопрос № 8
$$1 Find the limit of the function:
0.4
Вопрос № 9
$$1 Find the limit of the function:
-0.5
Вопрос № 10
$$1 Find the limit of the function:
*
Вопрос № 11
$$1 Find the limit of the function:
0
Вопрос № 12
$$1 Find the limit of the function:
1/2
Вопрос № 13
$$1 Find the limit of the function:
4
Вопрос № 14
$$1 Find the limit of the function:
8/3
Вопрос № 15
$$1 Derivative of multiplication is
f’g + g’f
Вопрос № 16
$$1 Derivative of division is
(f’g – g’f)g2
Вопрос № 17
$$1 Take derivative of the function:
21 * sin(14x - 2)
Вопрос № 18
$$1 Take derivative of the function:
5/2*sin(3+X)/sqrt(cos(x+3))
Вопрос № 19
$$1 Take derivative of the function:
(x-2) * lnx + (x2-4x+5) / 2x
Вопрос № 20
$$1 Take derivative of the function: )
1/sin(2x+7)
Вопрос № 21
$$1 Take derivative of the function:
3sqrt(5x-6)*ln3*5 / sqrt(sx-6)
Вопрос № 22
$$1 Take second order derivative of the function:
24x+10
Вопрос № 23
$$1 Take second order derivative of the function: y = sin(x2+7)
-4*sin(x2+7)
Вопрос № 24
$$1 Take derivative of the function: y = (ln(x))3
3lnx2/x
Вопрос № 25
$$1 Take derivative of the function: y = (lnx)2
2lnx/2
Вопрос № 26
$$1 Take derivative of the function: y =
1/(sqrt(tanx) * cos2x)
Вопрос № 27
$$1 Take derivative of the function: y =
28*cos(x-2 / x+5) / (x+5)2
Вопрос № 28
$$1 Take derivative of the function: y = tan().
neohota
Вопрос № 29
$$1 Take derivative of the function: y = cos()
neohota
Вопрос № 30
$$1 Take derivative of the function: y = cot()
neohota
Вопрос № 31
$$1 Find the interval where the function is increasing:
(-*; -3] [1; +*)
Вопрос № 32
$$1 Find the interval where the function is decreasing:
Never
Вопрос № 33
$$1 Find the extreme points of the function :
3 and 1
Вопрос № 34
$$1 Find the extreme points of the function :
4 and 2
Вопрос № 35
$$1 Find the extreme points of the function :
Only 3
Вопрос № 36
$$1 Find the interval where the function is concave up:
[-1; +*)
Вопрос № 37
$$1 Find the interval where the function is concave down:
(-*; -1]
Вопрос № 38
$$1 Find the points of inflection of the function:
(-1, 26/3)
Вопрос № 39
$$1 Find the interval where the function is concave up:
2 to +*
Вопрос № 40
$$1 Find the interval where the function is concave down:
-* to 2
Вопрос № 41
$$1 Find the points of inflection of the function:
(2, -25/3)
Вопрос № 42
$$1 Find the equations of the vertical asymptotes of the function:
X= -2, 2
Вопрос № 43
$$1 Find the equations of the vertical asymptotes of the function:
X = -5, 0 ,5
Вопрос № 44
$$1 Find the equations of the horizontal asymptotes of the function:
Y = * or no solution??
Вопрос № 45
$$1 Find the equations of the horizontal asymptotes of the function:
Y = 4
Вопрос № 46
$$1 Find the partial derivative of the function of two variables:
2xy + cosy + 2
Вопрос № 47
$$1 Find the partial derivative of the function of two variables:
x2 – cos(x+y) - 4
Вопрос № 48
$$1 $$1 Find the partial derivative of the function of two variables: + xy
2xsiny + y
Вопрос № 49
$$1 Find the partial derivative of the function of two variables:-x3y
x2cosy – x3
Вопрос № 50
$$1 $$1 Find the partial derivative of the function of two variables:
3x2cosy - 2
Вопрос № 51
$$1 Find the partial derivative of the function of two variables:
-x3siny + x
Вопрос № 52
$$1 Find the partial derivative of the function of two variables: -xy
2xlny - y
Вопрос № 53
$$1 Find the partial derivative of the function of two variables: +xy
x2/y + x
Вопрос № 54
$$1 Find the partial derivative of the function of two variables:
-sinx + y
Вопрос № 55
$$1 Find the partial derivative of the function of two variables:
Cos(xy) + 1/y
Вопрос № 56
$$1 Find the partial derivative of the function of two variables:
3x2
Вопрос № 57
$$1 Find the partial derivative of the function of two variables:
-siny
Вопрос № 58
$$1 $$1 Find the partial derivative of the function of two variables:
1/x
Вопрос № 59
$$1 Find the partial derivative of the function of two variables:
2y
Вопрос № 60
$$1 Evaluate the indefinite integral:
Cos (-2x +4) / 2
Вопрос № 61
$$1 Evaluate the indefinite integral:
ln (1+3x2) / 6
Вопрос № 62
$$1 Evaluate the indefinite integral:
ln(x3 + 8) / 3
Вопрос № 63
$$1 Evaluate the indefinite integral:
ln sinx
Вопрос № 64
$$1 Evaluate the indefinite integral:
/ 7
Вопрос № 65
$$1 Evaluate the indefinite integral:
(25x^2 + 4) / 10* ln2
Вопрос № 66
$$1 Evaluate the indefinite integral:
-cos(ex)
Вопрос № 67
$$1 Evaluate the indefinite integral:
-cos(lnx)
Вопрос № 68
$$1 Evaluate the indefinite integral:
Lnx + x3
Вопрос № 69
$$1 Evaluate the indefinite integral:
3x – 2 * ln2x
Вопрос № 70
$$1 Evaluate the indefinite integral:
¾ * ln4/3x
Вопрос № 71
$$1 Evaluate the indefinite integral:
-2/3 * Cos (x3+1)
Вопрос № 72
$$1 Formula of Integration by parts is:
udv = u*v - vdu
Вопрос № 73
$$1 What property of indefinite integrals is wrong:
???
Вопрос № 74
$$1 What property of indefinite integrals is wrong:
???
Вопрос № 75
$$1 Evaluate definite integral:
41/6
Вопрос № 76
$$1 Evaluate definite integral:
-22/3
Вопрос № 77
$$1 Evaluate definite integral:
Sin 90 = 1
Вопрос № 78
$$1 Evaluate definite integral:
-Cos 90 = 0
Вопрос № 79
$$1 Evaluate definite integral:
26/3
Вопрос № 80
$$1 Formula for area S enclosed between two curves y=f(x)
and y=g(x) determinates by formula:
integral(a to b)(g(x) – f(x))
Вопрос № 81
$$1 Formula that makes connection between definite and indefinite integrals is (Fundamental theorem):
Вопрос № 82
$$1 Find the area bounded between two curves:
integral(a to b)(g(x) – f(x))
Вопрос № 83
$$1 Find the area bounded between two curves:
37
Вопрос № 84
$$1 Find the area bounded between two curves:
Ne ohota
Вопрос № 85
$$1 Find the area bounded between two curves:
Ne ohota
Вопрос № 86
$$1 Find the area bounded between two curves:
Ne ohota
Вопрос № 87
$$1 Find the area bounded between two curves:
Ne ohota
Вопрос № 88
$$1 Find the area bounded between two curves:
Ne ohota
Вопрос № 89
$$1 Find the area bounded between two curves:
Ne ohota
Вопрос № 90
$$1 Find the area bounded between two curves:
Ne ohota
Вопрос № 91
$$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: .
10200 / 10 = 1020
Вопрос № 92
$$1Average value over interval (a; b) of continuous function is defined by integral: .
Find the average cost of the function: C(x) = if x –output is changed: .
95 / 5 = 19
Вопрос № 93
$$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: .
12 / 6 = 2
Вопрос № 94
$$1Average value over interval (a; b) of continuous function is defined by integral: .
Find the average demand of the function: D(x) = if x –output is changed: .
-88 / 4 = 22
Вопрос № 95
$$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: .
-14/3
Вопрос № 96
$$1 Gini index is coefficient of equality, it is defined by integral:
Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y =
1/7
Вопрос № 97
$$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.
3/5
Вопрос № 98
$$1 Gini index is coefficient of equality, it is defined by integral:
Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y = x5/2.
5/7
Вопрос № 99
$$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.
7/10
Вопрос № 100
$$1 Gini index is coefficient of equality, it is defined by integral:
Gini index = here y=f(x) is Lorenz curve. Determine the coefficient of equality if Lorenz curve is given: y = x5/3.
5/8
Вопрос № 101
$$1 Find the general solution of differential equation:
X3/3 – x2/2
Вопрос № 102
$$1 Find the general solution of differential equation:
-Cos (4x) / 4
Вопрос № 103
$$1 Find the general solution of differential equation:
Sin x
Вопрос № 104
$$1 Find the general solution of differential equation:
X6/36
Вопрос № 105
$$1 Find the general solution of differential equation:
e-Cos x
Вопрос № 106
$$1 Find the general solution of differential equation:
e5x+2/5
Вопрос № 107
$$1 Find the general solution of differential equation:
Kak integrate (1 / (sqrt(x) + x ))
Вопрос № 108
$$1 Find the general solution of differential equation:
Sqrt(2/3 * x3)
Вопрос № 109
$$1 Find the general solution of differential equation:
y = e(x^4)/4
Вопрос № 110
$$1 Find the general solution of differential equation:
x2/2
Вопрос № 111
$$1 Find the general solution of differential equation:
2x/ln2
Вопрос № 112
$$1 Find the general solution of differential equation:
e3^x/ln3
Вопрос № 113
$$1 Find the general solution of differential equation:
x4/4+x3/3
Вопрос № 114
$$1 Find the general solution of differential equation:
3Sqrt (-3*cosx)
Вопрос № 115
$$1 Find the general solution of differential equation:
3sqrt((3*Sin x /2)2 )
Вопрос № 116
$$1 Find the common term of the number series:
1/10n
Вопрос № 117
$$1 Find the common term of the number series:
1/5n
Вопрос № 118
$$1 Find the common term of the number series:
1/(3+n)
Вопрос № 119
$$1 Find the common term of the number series:
n/(n+2)
Вопрос № 120
$$1 Find the common term of the number series:
(n+2)/4n
Вопрос № 121
$$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:
a – true, b - true
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)
d
Вопрос № 126
$$1 What series among harmonic series is/are divergent:
a); b) ; c) ; d) ; e)
a
Вопрос № 127
$$1 What series among following series is/are convergent:
a); b) ; c) ; d) ; e)
b and e
Вопрос № 128
$$1 What series among following series is/are divergent:
a); b) ; c) ; d) ; e)
a, c, d
Вопрос № 129
$$1Determine the interval of convergence with radius of the following power series:
(-1/4; +1/4)
Вопрос № 130
$$1Determine the interval of convergence with radius of the following power series:
(-3/15, +3/15)
Вопрос № 131
$$1Determine the interval of convergence with radius of the following power series:
(-e, e)
Вопрос № 132
$$1Determine the interval of convergence with radius of the following power series:
0??
Вопрос № 133
$$1Determine the interval of convergence with radius of the following power series:
(-10, 10)
Вопрос № 134
$$1Determine the interval of convergence with radius of the following power series:
(-7, 7)
Вопрос № 135
$$1Determine the interval of convergence with radius of the following power series:
(-6, 6)
Вопрос № 136
$$1 Find general solution of differential equation:
x4/2
Вопрос № 137
$$1 Find general solution of differential equation:
ex^3/3
Вопрос № 138
$$1 Find general solution of differential equation:
x
Вопрос № 139
$$1 Find general solution of differential equation:
x2/2
Вопрос № 140
$$1 Find general solution of differential equation:
lnx
Вопрос № 141
$$1 Find general solution of differential equation:
e3x
Вопрос № 142
$$1 Find general solution of differential equation:
x3/3 + 4x
Вопрос № 143
$$1 Find general solution of differential equation:
-cosx
Вопрос № 144
$$1 Find general solution of differential equation:
x2/2 – 8x
Вопрос № 145
$$1 Find general solution of differential equation:
ex^2 – 3x
Вопрос № 146
$$1What series among following alternating series is/are divergent:
a); b) ; c) ; d) ; e)
a, c, d
Вопрос № 142
$$1What series among following alternating series is/are convergent absolutely:
a); b) ; c) ; d) ; e)
b, e
Вопрос № 143
$$1What series among following alternating series is/are convergent conditionally:
a); b) ; c) ; d) ; e)
b ,e
Вопрос № 144
$$1What series among following alternating series is/are convergent conditionally:
a); b); c) ; d) ; e)
b, d
Вопрос № 145
$$1What series among following alternating series is/are convergent absolutely:
a); b) ; c) ; d) ; e)
b, d
Вопрос № 146
$$1What series among following alternating series is/are divergent:
a); b) ; c) ; d) ; e)
a, c, e
Вопрос № 147
$$1 Evaluate the iterated integral:
11/3
Вопрос № 148
$$1 Evaluate the iterated integral:
8/3
Вопрос № 149
$$1 Evaluate the iterated integral:
23/3
Вопрос № 150
$$1 Evaluate the iterated integral:
-4/3 = 4/3
Вопрос № 151
$$1 Reduce the double integral to iterated integral: . D –region is depicted
100
Вопрос № 152
$$1 Reduce the double integral to iterated integral: . D –region is depicted
9/ln3 - 4
Вопрос № 153
$$1 Reduce the double integral to iterated integral : . D –region is depicted
4/3
Вопрос № 154
$$1 Reduce the double integral to iterated integral : . D –region is depicted
6/ln2 – 3ln3 + 2
Вопрос № 155
$$1 Reduce the double integral to iterated integral : . D –region is depicted
9
Вопрос № 156
$$1 Take the limit using L,Hopital,s rule :
0
Вопрос № 157
$$1 Take the limit using L,Hopital,s rule :
*
Вопрос № 158
$$1 Take the limit using L,Hopital,s rule :
*
Вопрос № 159
$$1 Take the limit using L,Hopital,s rule :
2
Вопрос № 160
$$1 Take the limit using L,Hopital,s rule :
6
Вопрос № 161
$$1 Take the limit using L,Hopital,s rule :
*
Вопрос № 162
$$1 Take the limit using L,Hopital,s rule :
ln5
Вопрос № 163
$$1 Take the limit using L,Hopital,s rule :
12/ln5
Вопрос № 164
$$1 Take the limit using L,Hopital,s rule :
*
Вопрос № 165
$$1 Take the limit using L,Hopital,s rule :
9/4
Вопрос № 166
$$1 Take the limit using L,Hopital,s rule :
0
Вопрос № 167
$$1 Take the limit using L,Hopital,s rule :
0
Вопрос № 168
$$1 Take the limit using L,Hopital,s rule :
(ln4)/3
Вопрос № 169
$$1 Take the limit using L,Hopital,s rule :
2ln5
Вопрос № 170
$$1 Take the limit using L,Hopital,s rule :
0
Вопрос № 171
$$1 Take the indefinite integral:
-1/Cos x
Вопрос № 172
$$1 Take the indefinite integral:
-3six/ln3
Вопрос № 173
$$1 Take the indefinite integral:
-Cos (lnx)
Вопрос № 174
$$1 Take the indefinite integral:
-esinx
Вопрос № 175
$$1 Take the indefinite integral:
-cos(3x2+7)/6
Вопрос № 176
$$1 Take the indefinite integral:
sin(5x2-3)/10
Вопрос № 177
$$1 Take the indefinite integral:
34x^2-3/(8ln3)
Вопрос № 178
$$1 Take the indefinite integral:
tan3x/3
Вопрос № 179
$$1 Take the indefinite integral:
cot3x/3
Вопрос № 180
$$1 Take the indefinite integral:
tan3x/3
Вопрос № 181
$$1 Which of the following functions is inverse to the function:
arctanx
Вопрос № 182
$$1 Which of the following functions is inverse to the function:
arccotx
Вопрос № 183
$$1 Which of the following functions is inverse to the function:
arcsinx
Вопрос № 184
$$1 Which of the following functions is inverse to the function:
arccosx
Вопрос № 185
$$1 Which of the following functions is inverse to the function:
ex
Вопрос № 186
$$1 Which of the following functions is inverse to the function:
lnx
Вопрос № 187
$$1 Which of the following functions is inverse to the function:
sinx
Вопрос № 188
$$1 Which of the following functions is inverse to the function:
cosx
Вопрос № 189
$$1 Which of the following functions are even functions:
a) ; b) ; c) d) e)
a, d, e
Вопрос № 190
$$1 Which of the following functions are odd functions:
a) ; b) ; c) d) e)
b, c
Вопрос № 191
$$1 Take differential of the function:
6sin2(2x+6)*cos(2x+6)
Вопрос № 192
$$1 Take differential of the function:
cos(lnx + 6) / x
Вопрос № 193
$$1 Take differential of the function:
24x*(3x2+7)3
Вопрос № 194
$$1 Take differential of the function:
6x/(3x2-x)
Вопрос № 195
$$1 Take differential of the function:
3/(2*sqrt(3x+5))
Вопрос № 196
$$1 Take differential of the function:
Cos x * 3sinx
Вопрос № 197
$$1 Take differential of the function:
-sinx * 5cosx
Вопрос № 198
$$1 Take differential of the function:
1/(cos2(sqrt(x))*2sqrt(x))
Вопрос № 199
$$1 Take differential of the function:
1/2x
Вопрос № 200
$$1 Take differential of the function:
3sqrt(x)/ 2sqrt(x)
Вопрос № 201
$$1 Test the function of two variables on extreme points:
(1, 1)
Вопрос № 202
$$1 Test the function of two variables on extreme points:
(0.-2)
Вопрос № 203
$$1 Test the function of two variables on extreme points:
(2, -3)
Вопрос № 204
$$1 Test the function of two variables on extreme points:
(4, -2)
Вопрос № 205
$$1 Test the function of two variables on extreme points:
(2, 3)