1. Find the area of convergence of the series. (1-3)
 
4. Arrange the Maclaurin function f (x). Specify the region of convergence of the series obtained for this function.
4.15. f (x) = xcos√x

5. Calculate the approximate value specified with a given degree of accuracy α, using power series expansion appropriately chosen function
5.15. 6√738, α = 0,001

6. I Am using the expansion of the integrand in a power series, calculate the definite integral said up to 0,001.

7. Find a power series expansion in powers of x solving the differential equation (record the first three non-zero, a member of this expansion)
7.15. y '= ycosx + 2cosy, y (0) = 0

8. The method of successive differentiation to find the first k terms of the expansion in a power series solutions of differential equations at the specified initial conditions.
8.15. y '' = y '/ y - 1 / x, y (1) = 1, y' (1) = 0, k = 4

Detailed solution. Designed in PDF format for easy viewing of IDZ solutions on smartphones and PCs. In MS Word (doc format) sent additionally.