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.
4.29 f (x) = sinx, x0 = a
5. Calculate the approximate value specified with a given degree of accuracy α, using power series expansion appropriately chosen function
5.29. 1 / 7√136, 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)
7.29. y ´= x2 + 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.
8.29. 4x2y ´´ + y = 0, y (1) = 1, y ´(1) = 1/2, k = 3