Chapter 2 - Limits - 2.7 Limits at Infinity - Exercises - Page 82: 15

$$\infty $$

\begin{align*} \lim _{x \rightarrow -\infty}\frac{3x^3-10}{ x+4}&= \lim _{x \rightarrow -\infty}\frac{x^3}{x}\frac{3-10x^{-3}}{ 1+4x^{-1}}\\ &=\lim _{x \rightarrow -\infty}\frac{x^3}{x}\lim _{x \rightarrow -\infty}\frac{3-10x^{-3}}{ 1+4x^{-1}}\\ &=3\lim _{x \rightarrow -\infty} x^2 \\ &=\infty.\\ \end{align*}