## University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson

# Chapter 4 - Section 4.5 - Indeterminate Forms and L'Hôpital's Rule - Exercises - Page 248: 37

#### Answer

$\ln 2$

#### 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, $\lim\limits_{x \to \infty} f(\infty)=\lim\limits_{x \to \infty} \ln (\dfrac{2x}{x+1})=\dfrac{\infty}{\infty}$ This shows an indeterminate form of the limit, so we need to use L'Hospital's rule. Here, $A'(x)=2$ and $B'(x)=1$ $\lim\limits_{x \to \infty} \dfrac{2}{1}=\ln 2$

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