Answer
$=\frac{1}{3}$
Work Step by Step
$\lim\limits_{x \to 0}\frac{tanx-x}{x^{3}}=\lim\limits_{x \to 0}\frac{(x+\frac{1}{3}x^{3}+\frac{2}{15}x^{5}+....)-x}{x^{3}}$
$=\lim\limits_{x \to 0}(\frac{1}{3}+\frac{2}{15}x^{2}+...)$
$=\frac{1}{3}$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
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
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