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: 16



Work Step by Step

Since $$ \lim _{x \rightarrow \infty} \frac{ x^2 }{e^x}=\frac{\infty}{\infty} $$ is an intermediate form, then we can apply L’Hôpital’s Rule as follows $$ \lim _{x \rightarrow \infty} \frac{ x^2 }{e^x}=\lim _{x \rightarrow \infty} \frac{ 2x }{e^x}=\frac{\infty}{\infty}. $$ Again, by applying L’Hôpital’s Rule, we get $$ \lim _{x \rightarrow \infty} \frac{ 2x }{e^x}=\lim _{x \rightarrow \infty} \frac{ 2 }{e^x}=\frac{2}{\infty}=0. $$
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