Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 72: 26

$$0$$

\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}