Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 8

(a)$\frac{3}{4} $ (b)$\frac{3}{4} $

(a)\begin{align*} \lim _{x \rightarrow \infty} \frac{3-(2 / x)}{4+\left(\sqrt{2} / x^{2}\right)}&=\frac{3-\lim _{x \rightarrow \infty}(2 / x)}{4+\lim _{x \rightarrow \infty}\left(\sqrt{2} / x^{2}\right)}\\ &=\frac{3-0}{4+0}\\ &= \frac{3}{4} \end{align*} (b)\begin{align*} \lim _{x \rightarrow-\infty} \frac{3-(2 / x)}{4+\left(\sqrt{2} / x^{2}\right.}&=\frac{3-\lim _{x \rightarrow-\infty}(2 / x)}{4+\lim _{x \rightarrow-\infty}\left(\sqrt{2} / x^{2}\right)}\\ &=\frac{3-0}{4+0}\\ &=\frac{3}{4} \end{align*}