Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - Chapter Review Exercises - Page 388: 118



Work Step by Step

Since \begin{align*} \lim _{x \rightarrow 1} \frac{\sqrt{1-x^{2}}}{\cos ^{-1} x}&=\frac{0}{0} \end{align*} Then by using L’Hôpital’s Rule \begin{align*} \lim _{x \rightarrow 1} \frac{\sqrt{1-x^{2}}}{\cos ^{-1} x}\\ &= \lim _{x\to \:1}\left(\frac{-\frac{x}{\sqrt{1-x^2}}}{-\frac{1}{\sqrt{1-x^2}}}\right)\\ &= \lim _{x\to \:1}\left(x\right)\\ &=1 \end{align*}
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