Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.6 Calculating Limits Using the Limit Laws - 1.6 Exercises - Page 71: 39


$\lim\limits_{x \to 0}x^{4}cos \frac{2}{x}=0$

Work Step by Step

$\lim\limits_{x \to 0}x^{4}cos \frac{2}{x}$ $-1\leq cos \frac{2}{x}\leq1$ therefore $-x^{4}\leq x^{4} cos \frac{2}{x}\leq x^{4} $ and $\lim\limits_{x \to 0}x^{4}=0$ $\lim\limits_{x \to 0}-x^{4}=0$ Therefore by the squeeze theorem : $\lim\limits_{x \to 0}x^{4}cos \frac{2}{x}=0$
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