Chapter 2 - Limits - 2.7 Limits at Infinity - Exercises - Page 82: 14

$$0$$

\begin{align*} \lim _{x \rightarrow -\infty}\frac{5x-9}{4x^3+2x+7}&= \lim _{x \rightarrow -\infty}\frac{x}{x^3}\frac{5-9x^{-1}}{4+2x^{-2}+7^{-3}}\\ &=\lim _{x \rightarrow -\infty}\frac{x}{x^3}\lim _{x \rightarrow -\infty}\frac{5-9x^{-1}}{4+2x^{-2}+7^{-3}}\\ &=\frac{5}{4}\lim _{x \rightarrow -\infty} x^{-2} \\ &=0.\\ \end{align*}