Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 7

(a)$\frac{-5}{3} $ (b)$\frac{-5}{3} $

(a)\begin{align*} \lim _{x \rightarrow \infty} \frac{-5+(7 / x)}{3-\left(1 / x^{2}\right)}&=\frac{-5+\lim _{x \rightarrow \infty}(7 / x)}{3-\lim _{x \rightarrow \infty}\left(1 / x^{2}\right)}\\ &=\frac{-5+0}{3-0}\\ &=\frac{-5}{3} \end{align*} (b)\begin{align*} \lim _{x \rightarrow-\infty} \frac{-5+(7 / x)}{3-\left(1 / x^{2}\right)}&=\frac{-5+\lim _{x \rightarrow-\infty}(7 / x)}{3-\lim _{x \rightarrow-\infty}\left(1 / x^{2}\right)}\\ &=\frac{-5+0}{3-0}\\ &=\frac{-5}{3} \end{align*}