Mathematics Synergy 1 course (Elements of higher mathem

Mathematics Synergy 1 course (Elements of higher mathematics) score 90/100 points

For questions with formulas, see the pictures in the product description

1.The Gauss method for solving a system of linear equations involves the use of ...
algebraic addition
system determinants
Formulas for calculating unknowns
successive elimination of unknowns

2. Find the limit: the formula in the picture

3.Calculate the definite integral: the formula in the picture

4. Find: the formula in the picture

5 find the limit: the formula in the picture

6.Find: the formula in the picture

7.Among the listed differential equations, indicate the homogeneous equation: the formula in the picture

8. The equation y "- 4y = ex is ...
differential Bernoulli equation
linear inhomogeneous differential equation of the second order with constant coefficients
linear homogeneous differential equation of the second order with constant coefficients
differential equation with separable variables

9.Write the canonical equation of the ellipse if its semiaxes are given: a = 5 and b = 4

10. Make an equation for the plane, knowing that point A (1, -1.3) is the base of the perpendicular drawn from the origin to this plane.
x-y 3z-11 = 0
-x y 3z-11 = 0
x-y-3z 11 = 0
x-y 11z-3 = 0

11.The vertices of the triangle ABC are given: A (3; -1), B (4; 2) and C (-2; 0). Indicate the equations of its sides
1) i - y 10 = 0, Zx - Zy 2 = 0, x 5y 2 = 0
2) Zy - y = 0, zy - 6 = 0, x - 5y 3 = 0
3) Zx-y- 10 = 0, i - Zy 2 = 0, i 5y 2 = O

12. Find the derivative of the function y = helx - elx
heh
elh
helkh

13 find the limit

14 find the limit: the formula in the picture

15. Find the maximum (minimum) points of the function y = xl2 - 2x
0; -1) - maximum point
1; -1) - maximum point
1; -1) - minimum point

16.Calculate the limit by L'Hôpital's rule: the formula in the picture

17.Specify a natural series of numbers
-1, -2, -3, -4, -5, -6, -7, -8. -nine
-9, -8, -7, -6, -5, -4, -3, -2, -1, O, 1, 2, 3, 4, 5, b, 7, 8, 9, ...
0, 1, 2, 3, 4, 5, b, 7, 8, 9, ...
1, 2, 3, 4, 5, b, 7, 8, 9 ..

18 find the limit: the formula in the picture

19 find the limit: the formula in the picture

20. Find the limit: the formula in the picture

21 Find the area of ​​the figure enclosed between the straight lines y = 4x - 5, x = -3, x = -2 and the Ox axis
fifteen
12
ten
7

22. Find the general solution to the equation xyA2dy = (xA3 yA3) dx
y3 = 3x3 ln | Cx |
у3 = Зх3 ln | Cx
у3 = Зх3 ln Cx

23 Calculate the determinant: the formula in the picture
-20
20
ten
-ten

24. Find the derivative of the function y = 2tgx

25.Specify the equation of a circle for which points A (3: 2) and B (-1; 6) are the ends of one of the diameters
(X- 1) l2 - (y 4) l2 = 8
(X - 1) l2 (y - 4) l2 = 8
(X- 1) l2- (y 4) l2 = 64
(X- 1) l2 (y-4) l2 = 16

26. Find the equation of the straight line passing through the point of intersection of lines 2x Zu-8 = 0x-4y 5 = 0 and through the point M1 (-2; 3)
5x 13u-29 = 0
5x 3y-29 = 0
5x 13y-9 = 0
Zx 8y-18 = 0

27 Calculate the determinant: the formula in the picture

28. Given points M (-5; 7; -6), N (7; -9; 9). Calculate the projection of the vector a = {1; -3; 1} to the vector MN
4
25
75
3

29. Find the limit lim (1-5 / x) x
ate3
ate2
eat5
eat-5

30. The determinant of a system of three linear inhomogeneous equations with three unknowns is 5. This means that ...
the system has a zero solution
the system has many solutions
the system has no solution
the system has only one solution