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: 16


$$-\infty $$

Work Step by Step

\begin{align*} \lim _{x \rightarrow -\infty}\frac{2x^5+3x^4-31x}{8 x^4-31x^2+12}&= \lim _{x \rightarrow -\infty}\frac{x^5}{x^4}\frac{2 +3x^{-1}-31x^{-4}}{8 -31x^{-2}+12x^{-4}}\\ &=\lim _{x \rightarrow -\infty}\frac{x^5}{x^4}\lim _{x \rightarrow -\infty}\frac{2 +3x^{-1}-31x^{-4}}{8 -31x^{-2}+12x^{-4}}\\ &=\frac{2}{8}\lim _{x \rightarrow -\infty} x \\ &=-\infty. \end{align*}
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