Answer
$$\infty$$
Work Step by Step
We evaluate the limit:
\begin{align*}
\lim _{x \rightarrow 1+}\left(\frac{1}{\sqrt{x-1}}-\frac{1}{\sqrt{x^{2}-1}}\right)&=\lim _{x \rightarrow 1+} \frac{\sqrt{x+1}-1}{\sqrt{x^{2}-1}}\\
&=\infty
\end{align*}
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 2 - Limits - Chapter Review Exercises - Page 94: 43
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