University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.5 - Indeterminate Forms and L'Hôpital's Rule - Exercises - Page 249: 82



Work Step by Step

L'Hospital's rule states that $\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} \dfrac{A'(x)}{B'(x)}$ Here, $\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} (\sqrt {x^3+1}-\sqrt x)$ or, $\lim\limits_{x \to \infty} (\sqrt {x^3+1}-\sqrt x)=\lim\limits_{x \to \infty} x (\dfrac{\sqrt {x^3+1}}{x}-\dfrac{\sqrt x}{x})$ or, $\lim\limits_{x \to \infty} (\sqrt {1+1/x^2}-\sqrt{\dfrac{1}{x}})=\lim\limits_{x \to \infty} (x)(1)=\infty$
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.