Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 6

(a)$ \frac{1}{8} $ (b)$ \frac{1}{8} $

(a)\begin{align*} \lim _{x \rightarrow \infty} \frac{1}{8-\left(5 / x^{2}\right)}&=\frac{1}{8-\lim _{x \rightarrow \infty}\left(5 / x^{2}\right)}=\frac{1}{8-0}\\ &=\frac{\left[\frac{1}{8}\right]}{8-0}=\frac{\left[\frac{1}{8}\right]}{8}\\ &= \frac{1}{8} \end{align*} (b)\begin{align*} \lim _{x \rightarrow-\infty} \frac{1}{8-\left(5 / x^{2}\right)}&=\frac{1}{8-\lim _{x \rightarrow-\infty}\left(5 / x^{2}\right)}\\ &=\frac{1}{8-0}\\ &= \frac{1}{8} \end{align*}