IDZ 12.2 - Option 30. 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.
4.30 f (x) = ln (5x + 3), x0 = 1

5. Calculate the approximate value specified with a given degree of accuracy α, using power series expansion appropriately chosen function
5.30. 1 / 3√e, 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)
7.30. y ´= x2 + y, 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.
8.30. y ´= 2x2 + y3, y (1) = 1, k = 3