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: 25



Work Step by Step

\begin{align*} \lim _{x \rightarrow 4}\left(\frac{1}{\sqrt{x}-2}-\frac{4}{x-4}\right)&=\lim _{x \rightarrow 4} \frac{\sqrt{x}+2-4}{(\sqrt{x}-2)(\sqrt{x}+2)}\\ &=\lim _{x \rightarrow 4} \frac{\sqrt{x}-2}{(\sqrt{x}-2)(\sqrt{x}+2)}\\ &=\frac{1}{4} \end{align*}
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