Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 11 - Section 11.10 - Taylor and Maclaurin Series - 11.10 Exercises - Page 772: 66



Work Step by Step

$\lim\limits_{x \to 0}\frac{tanx-x}{x^{3}}=\lim\limits_{x \to 0}\frac{(x+\frac{1}{3}x^{3}+\frac{2}{15}x^{5}+....)-x}{x^{3}}$ $=\lim\limits_{x \to 0}(\frac{1}{3}+\frac{2}{15}x^{2}+...)$ $=\frac{1}{3}$
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