Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.3 Basic Limit Laws - Exercises - Page 59: 35


See the example below.

Work Step by Step

Let $ f(x)=g(x)=\frac{1}{x}$. One can see that $\lim\limits_{x \to 0}f(x)$ and $\lim\limits_{x \to 0}g(x)$ do not exist (because we can not divide by $0$). But the limit $\lim\limits_{x \to 0}(f(x)/g(x))$ does exist: $$\lim\limits_{x \to 0}(f(x)/g(x))=\lim\limits_{x \to 0}(1)=1.$$
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