Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 72: 33



Work Step by Step

\begin{align*} \lim _{\theta \rightarrow \frac{\pi}{4}}\left(\frac{1}{\tan \theta-1}-\frac{2}{\tan ^{2} \theta-1}\right)&=\lim _{\theta \rightarrow \frac{\pi}{4}} \frac{(\tan \theta+1)-2}{(\tan \theta+1)(\tan \theta-1)}\\ &=\lim _{\theta \rightarrow \frac{\pi}{4}} \frac{1}{\tan \theta+1}\\ &=\frac{1}{2} \end{align*}
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