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Suppose a function f(x) has the power series representation n = 0 i n f i n i t y x n / n We

Suppose a function f(x) has the power series representation n=0infinityxn / n

We have f(x) = n=0infinityxn /n

a) First find the radius of convergence of the power series representation of f(x).

b) Find the power series representation for f'(x) and its interval of convergence.

c)Find the antiderivative of the function f(x) and its radius of convergence.

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