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: 36



Work Step by Step

We have $$ \lim _{x \rightarrow 2}\frac{e^{x^2}-e^4}{x-2}=\frac{0}{0} $$ is an intermediate form, then we can apply L’Hôpital’s Rule as follows $$\lim _{x \rightarrow 2}\frac{e^{x^2}-e^4}{x-2}=\lim _{x \rightarrow 2}\frac{2xe^{x^2}}{1}=4e^4.$$
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