Find the general solution of the differential equation allowing reduction of order
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) 
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) 
28. Calculate the triple integral 
a) 
29. 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
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)
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
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) 