Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.3 - Calculating Limits Using the Limit Laws - 2.3 Exercises - Page 104: 60


a) $\lim\limits_{x \to 0}f(x)=0$ b) $\lim\limits_{x \to 0}\frac{f(x)}{x}=0$

Work Step by Step

a) $\lim\limits_{x \to 0} \frac{f(x)}{x^2}=5$ $\frac{\lim\limits_{x \to 0}f(x)}{\lim\limits_{x \to 0}x^2}=5$ $\lim\limits_{x \to 0}f(x)=5\lim\limits_{x \to 0} x^2=5\times0=0$ b) $\lim\limits_{x \to 0} \frac{f(x)}{x^2}=5$ $\frac{\lim\limits_{x \to 0}f(x)}{\lim\limits_{x \to 0}x^2}=5$ $\frac{\lim\limits_{x \to 0}f(x)}{(\lim\limits_{x \to 0}x)^2}=5$ $\frac{\lim\limits_{x \to 0}f(x)}{\lim\limits_{x \to 0}x}=5\lim\limits_{x \to 0}x$ $\lim\limits_{x \to 0}\frac{f(x)}{x}=5\lim\limits_{x \to 0}x=5\times0=0$
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