Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 55: 58



Work Step by Step

Given $$\lim _{\theta \rightarrow 0} \frac{\sin ^{2} 4 \theta}{\cos \theta-1}$$ Consider $$ f(\theta)= \frac{\sin ^{2} 4 \theta}{\cos \theta-1}$$ From the following figure, we can observe that \begin{align*} \lim _{\theta\rightarrow 0^+} f( \theta)&=-31.98\\ \lim _{\theta \rightarrow 0^-} f( \theta)&=-31.98 \end{align*} Then $$\lim _{\theta \rightarrow 0} \frac{\sin ^{2} 4 \theta}{\cos \theta-1}=-31.98$$
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