Control 2,3 and 4 on higher mathematics (MSTUCA)

Examination №2
Task 6.
Find the limits of the functions without using the rule of L'Hospital.
a B C)
d) d)
Task 7.
Find the derivatives of these functions.
a B C)
d) d) e)
Task 8.
Find for the given functions:
a); b)
Task 9.
Explore the features and methods of differential calculus on the basis of their build schedules.
a); b)

Examination №3
Task 11.
Find indefinite integrals. In part a) and b) to check the results of differentiation.
a); b); c); g)
Task 12.
Calculate the approximate value of the definite integral using Simpson's formula, dividing the interval of integration into 10 parts. All calculations are performed with rounding to the third decimal place.
Task 13.
Evaluate the improper integral or prove its divergence.
Task 14.
Calculate the area of \u200b\u200bthe figure bounded by parabolas.

Examination №4
Task 15.
Show that if.
Task 16.
Find grad (z) at the point A and the derivative at the point A in the direction of the vector, if A (1, 1).
Task 17.
Calculate the line integral, where L - ellipse.
Task 18.
Record D set limiting its curves - surface density. With the help of a double integral in polar coordinates to find the mass of the plate. Make a drawing.
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Task 19.
Calculate using the triple integral volume of the body bounded by said surfaces. Make a drawing of the body and its projection on the plane HOY.
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