Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.5 - Indeterminate Forms and L'Hopital's Rule - Exercises 7.5 - Page 409: 45



Work Step by Step

Here, we have $\lim\limits_{t \to \infty} f(\infty)=\dfrac{\infty}{\infty}$ This shows an indeterminate form of limit, thus we will apply L-Hospital's rule such as: $\lim\limits_{x \to \infty} f(x)=\lim\limits_{x \to \infty} \dfrac{p'(x)}{q'(x)}$ $\lim\limits_{t \to \infty} \dfrac{e^t+2t}{e^t-1}=\dfrac{e^{\infty}+2(\infty)}{e^{\infty}-1}=\dfrac{\infty}{\infty}$ Now, again apply L-Hospital's rule. $\lim\limits_{t \to \infty} \dfrac{e^t}{e^t}=1$
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.