Calculus (3rd Edition)

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

Chapter 2 - Limits - Chapter Review Exercises - Page 95: 49



Work Step by Step

We evaluate the limit: \begin{align*} \lim _{x \rightarrow 0} \frac{\cos x-1}{\sin x}&=\lim _{x \rightarrow 0} \frac{\cos x-1}{\sin x} \cdot \frac{\cos x+1}{\cos x+1}\\ &=\lim _{x \rightarrow 0} \frac{-\sin ^{2} x}{\sin x(\cos x+1)}\\ &=-\lim _{x \rightarrow 0} \frac{\sin x}{\cos x+1}\\ &=-\frac{0}{1+1}=0 \end{align*}
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