IDZ 12.2 - Option 5. 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.
4.5. f (x) = cos2x3 / 3

5. Calculate the approximate value specified with a given degree of accuracy α, using power series expansion appropriately chosen function
5.5. arctgπ / 10, 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)
7.5. y ´= x + 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.
8.5. yIV = xy + y´x2 y (0) = y ´(0) = y´ ´(0) = 1, y´ ´´ (0) = 1, k = 7