Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 27

$$0$$

\begin{align*} \lim _{x \rightarrow \infty} \frac{2 \sqrt{x}+x^{-1}}{3 x-7} : \frac{x}{x}&=\lim _{x \rightarrow \infty} \frac{\frac{2}{\sqrt{x}}+\frac{1}{x^{2}}}{3-\frac{7}{x}}\\ &= \frac{\lim _{x \rightarrow \infty} \frac{2}{\sqrt{x}}+\lim _{x \rightarrow \infty} \frac{1}{x^{2}}}{\lim _{x \rightarrow \infty} 3-\lim _{x \rightarrow \infty} \frac{7}{x}}\\ &= \frac{0+0}{3-0}\\ &=0 \end{align*}