University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 4 - Practice Exercises - Page 278: 83



Work Step by Step

Consider $f(x)=L=\lim\limits_{x \to \infty}(1+\dfrac{b}{x})^{kx}$ or, $\ln L=k\lim\limits_{x \to \infty} x \ln (1+\dfrac{b}{x})$ or, $\ln L=k \lim\limits_{x \to \infty} \dfrac{\ln (1+\dfrac{b}{x})}{1/x}$ Thus, $f(0)=\dfrac{0}{0}$ This shows an Inderminate form of the limit, so apply L'Hospital's rule: $\lim\limits_{x \to l}\dfrac{a(x)}{b(x)}=\lim\limits_{x \to l}\dfrac{a'(x)}{b'(x)}$ Thus, $\ln L=k \lim\limits_{x \to \infty} \dfrac{bx}{x+b}=kb$ or, $L=e^{kb}$
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.