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: 26



Work Step by Step

\begin{aligned} \lim _{x \rightarrow 0+} \frac{\sqrt{x+1}-1}{\sqrt{x} \sqrt{x+1} }&=\lim _{x \rightarrow 0+} \frac{(\sqrt{x+1}-1)(\sqrt{x+1}+1)}{\sqrt{x} \sqrt{x+1}(\sqrt{x+1}+1)}\\ &=\lim _{x \rightarrow 0+} \frac{x}{\sqrt{x} \sqrt{x+1}(\sqrt{x+1}+1)}\\ &=\lim _{x \rightarrow 0+} \frac{\sqrt{x}}{\sqrt{x+1}(\sqrt{x+1}+1)}\\ &=0 \end{aligned}
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