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: 32


$$ x-\dfrac{7}{6} x^3+\dfrac{61}{120} x^5-\dfrac{1247}{5040} x^7+....$$

Work Step by Step

Recall the Taylor series for $\cos x=1-\dfrac{ x^2}{2!}+\dfrac{x^4}{4!}-....$ and $\sin x= x-\dfrac{x^3}{3!}+\dfrac{ x^5}{5!}-....$ $\cos^2 x \sin x =[1-\dfrac{ x^2}{2!}+\dfrac{x^4}{4!}-....] \times [x-\dfrac{x^3}{3!}+\dfrac{ x^5}{5!}-....]$ or, $\cos^2 x \sin x =x-\dfrac{7}{6} x^3+\dfrac{61}{120} x^5-\dfrac{1247}{5040} x^7+....$
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