Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 27

$$-\infty$$

Given $$\lim _{x \rightarrow -\infty}\left(x^2+2x^7\right)$$ Then \begin{aligned} \lim _{x \rightarrow -\infty}\left(x^2+2x^7\right)&=\lim _{x \rightarrow -\infty}x^7\left(\frac{x^2}{x^7}+2 \right)\\ &=\lim _{x \rightarrow -\infty}x^7\left(\frac{1}{x^5}+2 \right)\\ &=\lim _{x \rightarrow -\infty}x^7\lim _{x \rightarrow -\infty}\left(\frac{1}{x^5}+2 \right)\\ &=(-\infty)(2)\\ &=-\infty \end{aligned}