Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.9 - Convergence of Taylor Series - Exercises 10.9 - Page 625: 12



Work Step by Step

Consider the Maclaurin Series for $\sin x$ is defined as: $ \sin x=x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!}-\dfrac{x^7}{7!}+...$ Multiply the above series with $x^2$ as follows: Then $x^2 \sin x=x^2 (x-\dfrac{x^3}{3!}+\dfrac{x^5}{5!}-\dfrac{x^7}{7!}+...)$ $\implies x^3-\dfrac{1}{3!}x^5+\dfrac{1}{5!}x^7-\dfrac{1}{7!}x^9+...$
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