IDZ 12.2 - Option 1. Decisions Ryabushko AP

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.
4.1. f (x) = cos5x

5. Calculate the approximate value specified with a given degree of accuracy α, using power series expansion appropriately chosen function
5.1. e, 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)
7.1. y ´= xy + ey, 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.
8.1. y ´= arcsiny + x, y (0) = 1/2, k = 4