Блок 1- Математический анализ
1. 
a) 
2. If u and v are differentiable at x and if then the quotient is differentiable at x, and:
a) 
3. Antiderivative for the function 
is a function :
a) 
4. For the integral 
can be used Euler substitution in the following cases:
a) 
5. If 
is continuous on the segment [a,b] and F is it’s any antiderivative on this segment, then we have the equality:
a) 
6. Find domain of the function 
a) 
7. The differential of the n-th order function y=f(x) is called
a) 
8. The homogeneous linear differential equation of the n-th order has the form:
a) 
9. The inhomogeneous linear differential equation of the n-th order has the form:
a) 
10. For function 
correctly the following statement:
a) 
are vertical asymptotes
11. For function 
value 
belongs to the interval:
a) ( 
12. Intervals of convexity and concavity of function 
:
a) Curve is convex in the interval (0;1)
13. It is true the following equality:
a) 
14. 
a) 
15. Calculate the definite integral 
a) 
16. Find the particular solution of the differential equation 
, satisfying the initial condition 
a) 
17. Solve the differential equation 
a) 
18. Find the particular solution of the differential equation 
, satisfying the initial condition 
a) 
19. Calculate the double integral 
a) 
20. Calculate the triple integral 
a) 
21. A line x=3 is an asymptote for the function:
a) 
b) 
c) 
d) 
e) 
22. Find the total differential of the function 
a) 
23. Analyse the function of the extremum: 
a) 
24. Solve the differential equation 
a) 
25. Find the general solution of the differential equation allowing reduction of order y’’’=sinx+cosx
a) 
26. Find the general solution of the differential equation allowing reduction of order 
a) 
27. Calculate the double integral 
a) 
b) 
c) 7,5
d) ½
e) 9/4
28. Calculate the triple integral 
a) 
29. Expand in powers of the difference x-1 function y=x4-2x3+2x+2 by Taylor’s Formula:
a) X4-2x3+2x+2=2(x-1)3+(x-1)4
b) X4-2x3+2x+2=2+2(x-1)3+(x-1)4
c) X4-2x3+2x+2=2+2(x-1)3
d) X4-2x3+2x+2=2+(x-1)4
e) X4-2x3+2x+2=2(x-1)3
30. Calculate 
with accuracy 
a) 0,479
1. For function f(x)= 
correctly the following statement:
A) x=2 is a point of discontinuity of the first kind, jump
2. If u and v are differentiable functions of x, then their sum is differentiable at every point where u and y are both differentiable. At such points
a) (u(x)+v(x))’=u’(x)∙v’(x)
b) (u(x)+v(x))’=u’(x)-v’(x)
c) (u(x)∙v(x))’=u’(x)∙v(x)-u(x)v’(x)
d) 
’= 
, v(x0) 
e) (u(x)+v(x))’=u’(x)+v’(x)
3. Rational fraction 
can be written as:
A) 
+ 
+ 
4. Calculate the definite integral 
A) - 
5. Find domain of the function z= 
A) (x,y): 
6. Faithful equality for function y=e2x-1
A) yn(0)=4e
7. Intervals of monotonicity of function y=(x+1)(x-2)2:
A) (-∞;1) decreases monotonically
8. It is true the following equality:
A) 
= 
ln 
+ C
9. Rational fraction 
can be written as:
A) 
+ 
+ 
10. Calculate the definite integral 
A) ln2
11. Calculate the double integral 
A) 4 
12. Calculate the triple integral 
A) 4
13. Function properties y= 
:
A) Points of discontinuity x=1; x=-1
14. Find the total differential of the function z=arctg 
+arctg 
A) dz=0
15. Determine the function of the extrmum: z=x2+xy+y2-3x-6y.
A) zmin=z(0;3)=-9
16. Solve the differential equation yx2dy-lnxdx=0
A) 
= - 
(lnx+1)+C, C-const
17. Find the general solution of the differential equation allowing reduction of order
y’’=x2-2x
A) y= 
- 
+C1 x+C2 , C1, C2-const
18. Calculate the double integral 
.
A) ln 
19. Calculate the triple integral 
A) 
(ln2+ 
)
20. Find the area of convergence of the power series 
A) 
21. Find the sum of the series x+ 
+ 
+…+ 
+…
A) S(x)= 
dx = ln 
22. Function 
is continuous at point 
if :
a) A) 
11. Faithful equality for function 
:
B) 
12. Intervals of convexity and concavity of function 
:
C)curve is convex in the interval (0;1)
13. 
=
A) xsinx +cosx +c
15.Calculate the definite integral 
B)arctge - 
19.Calculate the double integral 
:
C)4 
20.Calculate the triple integral 
A) 
21.Intervals of convexity and concavity of function 
E)curve is convex in the interval (-∞;1)
22. Find the partial derivatives 
of the function 
A) 
23.Find the differential 3rd order of function 
A) 
24.Solve the differential equation 
D) 
27.Calculate the double integral 
:
B)57 
29. Find the area of convergence of the power series 
C)[0,+∞)
30. Find the sum of the series 
A) 