Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 11 - Section 11.10 - Taylor and Maclaurin Series - 11.10 Exercises - Page 809: 75

Answer

$1+\frac{x^{2}}{6}+\frac{7x^{4}}{360}+...$

Work Step by Step

$y=\frac{x}{sinx}$ $sinx=x-\frac{x^{3}}{3!}+\frac{x^{5}}{5!}-....$ $\frac{x}{sinx}=\dfrac{x}{x-\frac{x^{3}}{3!}+\frac{x^{5}}{5!}-....}$ $\approx 1+\frac{x^{2}}{6}+\frac{7x^{4}}{360}+...$
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