Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.7 Limits at Infinity - Exercises - Page 82: 14



Work Step by Step

\begin{align*} \lim _{x \rightarrow -\infty}\frac{5x-9}{4x^3+2x+7}&= \lim _{x \rightarrow -\infty}\frac{x}{x^3}\frac{5-9x^{-1}}{4+2x^{-2}+7^{-3}}\\ &=\lim _{x \rightarrow -\infty}\frac{x}{x^3}\lim _{x \rightarrow -\infty}\frac{5-9x^{-1}}{4+2x^{-2}+7^{-3}}\\ &=\frac{5}{4}\lim _{x \rightarrow -\infty} x^{-2} \\ &=0.\\ \end{align*}
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