IDZ 12.2 - Option 25. 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.
4.25 f (x) = 1 / √4 + x, x0 = -3

5. Calculate the approximate value specified with a given degree of accuracy α, using power series expansion appropriately chosen function
5.25. 10√1080, 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)
7.25. y ´= xy + x2 + 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.
8.25. y ´´ = ycosy ´+ x, y (0) = 1, y´ (0) = π / 3, k = 3