IDZ 12.2 - Option 5. Decisions Ryabushko AP

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

• Arrange the Maclaurin function f (x). Specify the region of convergence of the series obtained for this function.

4.5. f (x) = cos2x3 / 3

• 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

• 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)

7.5. y '= x + 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.

8.5. yIV = xy + y'x2 y (0) = y '(0) = y' '(0) = 1, y' '' (0) = 1, k = 7

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