 # Control №2,3 and 4 on higher mathematics (MSTUCA)

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

Examination №3
Find indefinite integrals. In part a) and b) to check the results of differentiation.
a); b); c); g)
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.
Evaluate the improper integral or prove its divergence.
Calculate the area of \u200b\u200bthe figure bounded by parabolas.

Examination №4
Show that if.
Find grad (z) at the point A and the derivative at the point A in the direction of the vector, if A (1, 1).
Calculate the line integral, where L - ellipse.
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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