Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 10

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Given $$ \lim _{x\rightarrow \infty}\frac{1-x^2}{x^3-x+1}$$ Then \begin{aligned} \lim _{x\rightarrow \infty}\frac{1-x^2}{x^3-x+1} &= \lim _{x\rightarrow \infty}\frac{\frac{1}{x^3}-\frac{x^2}{x^3}}{\frac{x^3}{x^3}-\frac{x }{x^3}+\frac{1}{x^3}} \\ &= \lim _{x\rightarrow \infty}\frac{0-0}{1-0+0}\\ &=0 \end{aligned}