IDZ 12.2 - Option 21. Decisions Ryabushko AP

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.
4.21. f (x) = 1 / (x-3) 2, x0 = 1

5. Calculate the approximate value specified with a given degree of accuracy α, using power series expansion appropriately chosen function
5.21. lg7, 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)
7.21. y ´= xsinx - y2, y (0) = 1

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.
8.21. y ´´ = x2 + y2, y (-1) = 2, y ´(- 1) = 0,5, k = 4