Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.7 L'Hôpital's Rule - Exercises - Page 366: 20



Work Step by Step

We have $$ \lim _{x \rightarrow \infty} \frac{x^{2/3}+3x}{x^{5/2}-x}=\frac{\infty}{\infty}. $$ is an intermediate form, then we can apply L’Hôpital’s Rule as follows $$ \lim _{x \rightarrow \infty} \frac{x^{2/3}+3x}{x^{5/2}-x}=\lim _{x \rightarrow \infty} \frac{(2/3)x^{-1/3}+3}{(5/2)x^{3/2}-1}=\frac{0+3}{\infty}=0. $$
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