Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.4 - Indeterminate Forms and l''Hospital''s Rule - 4.4 Exercises - Page 312: 71

Answer

On the graph, we can see that both ratios have the same limit as $x \to 0$ $\lim\limits_{x \to 0}\frac{f(x)}{g(x)} = \frac{1}{4}$

Work Step by Step

On the graph, we can see that both ratios have the same limit as $x \to 0$ $\lim\limits_{x \to 0}\frac{f(x)}{g(x)} = \lim\limits_{x \to 0}\frac{e^x-1}{x^3+4x} = \frac{0}{0}$ We can apply L'Hospital's Rule. $\lim\limits_{x \to 0}\frac{f'(x)}{g'(x)} = \lim\limits_{x \to 0}\frac{e^x}{3x^2+4} = \frac{1}{0+4} = \frac{1}{4}$ Therefore: $\lim\limits_{x \to 0}\frac{f(x)}{g(x)} = \frac{1}{4}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.