Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 11

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Given $$ \lim _{x\rightarrow -\infty}\frac{x-2}{x^2 +1}$$ Then \begin{aligned} \lim _{x\rightarrow -\infty}\frac{x-2}{x^2 +1} &= \lim _{x\rightarrow-\infty}\frac{\frac{x}{x^2}-\frac{ 2}{x^2}}{\frac{x^2}{x^2} +\frac{1}{x^2}} \\ &= \lim _{x\rightarrow-\infty}\frac{\frac{1}{x }-\frac{ 2}{x^2}}{1 +\frac{1}{x^2}} \\ &= \lim _{x\rightarrow -\infty}\frac{0-0}{1 +0}\\ &=0 \end{aligned}