IDZ 12.2 - Option 25. Decisions Ryabushko AP

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• Find the area of convergence of the series. (1-3)

• 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

• 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

• I Am using the expansion of the integrand in a power series, calculate the definite integral said up to 0,001.

• 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

• 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

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