1. Find the area of convergence of the series. (1-3)
 
4. Arrange the function f (x) in a Taylor series in the neighborhood of this point x0. Find the area of convergence of the series obtained for this function.
4.19. f (x) = ex, x0 = 1

5. Calculate the approximate value specified with a given degree of accuracy α, using power series expansion appropriately chosen function
5.19. ln10, α = 0,0001

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)
7.19. y '= xy - y2, y (0) = 0.2

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.
8.19. y '' = eysiny ', y (π) = 1, y' (π) = π / 2, k = 3

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