Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 28

$$-1$$

\begin{align*} \lim _{x \rightarrow \infty} \frac{2+\sqrt{x}}{2-\sqrt{x}} : \frac{\sqrt{x}}{\sqrt{x}}&=\lim _{x \rightarrow \infty} \frac{\frac{2}{\sqrt{x}}+1}{\frac{2}{\sqrt{x}}-1}\\ &=\frac{\lim _{x \rightarrow \infty}\frac{2}{\sqrt{x}}+\lim _{x \rightarrow \infty}(1)}{\lim _{x \rightarrow \infty}\frac{2}{\sqrt{x}}-\lim _{x \rightarrow \infty}(1)}\\ &=\frac{0+1}{0-1}\\ &=-1 \end{align*}