Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 4 - Applications of the Derivative - 4.7 L'Hopital's Rule - 4.7 Exercises - Page 307: 6


The example is $$\lim_{x\to0}\frac{\ln x}{x^{-2}}$$

Work Step by Step

The example is $$\lim_{x\to0}\frac{\ln x}{x^{-2}}.$$ Indeed, for the numerator $$\lim_{x\to 0}\ln x=-\infty$$ for the denominator $$\lim_{x\to 0}x^{-2}=\lim_{x\to 0}\frac{1}{x^2}=\infty,$$ since when $x\to 0$ so we have the form $\infty/\infty$ as $x\to0$
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