Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.6 - Limits Involving Infinity; Asymptotes of Graphs - Exercises 2.6 - Page 97: 30

Answer

$\infty $

Work Step by Step

\begin{align*} \lim _{x \rightarrow \infty} \frac{x^{-1}+x^{-4}}{x^{-2}-x^{-3}} \cdot \frac{x^{2}}{x^{2}}&=\lim _{x \rightarrow \infty} \frac{x+x^{-2}}{1-x^{-1}}\\ &= \frac{\lim _{x \rightarrow \infty}x+\lim _{x \rightarrow \infty}x^{-2}}{\lim _{x \rightarrow \infty}(1)-\lim _{x \rightarrow \infty}x^{-1}}\\ &=\frac{\infty+0}{1-0}\\ &=\infty \end{align*}
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