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Solution: Differentiating and integrating power series Find
Chapter 8, Problem 36E(choose chapter or problem)
Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.
\(g(x)=\frac{x}{\left(1+x^{2}\right)^{2}}\) using \(f(x)=\frac{1}{1+x^{2}}\)
Questions & Answers
QUESTION:
Differentiating and integrating power series Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series.
\(g(x)=\frac{x}{\left(1+x^{2}\right)^{2}}\) using \(f(x)=\frac{1}{1+x^{2}}\)
ANSWER:Solution 36EStep 1:In this problem we need to find the the power series representation for centered at 0 by differentiating or integrating the power series for We already know a power series for ,namely for Therefore power series representation for is