Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 242: 28


$$ \infty$$

Work Step by Step

Given $$\lim _{x \rightarrow -\infty}\frac{1+x^6}{x^4+1}$$ Then \begin{aligned} \lim _{x \rightarrow -\infty}\frac{1+x^6}{x^4+1}&=\lim _{x \rightarrow -\infty}\frac{1/x^4+x^6/x^4}{x^4/x^4+1/x^4} \\ &=\frac{\lim _{x \rightarrow -\infty}(1/x^4)+\lim _{x \rightarrow -\infty}(x^2)}{\lim _{x \rightarrow -\infty}(1)+\lim _{x \rightarrow -\infty}(1/x^4)}\\ &=\lim _{x \rightarrow -\infty}(x^2)\\ &= \infty \end{aligned}
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