University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 4 - Practice Exercises - Page 277: 70



Work Step by Step

Consider $f(x)=\lim\limits_{x \to 0} (\dfrac{1}{x^4}-\dfrac{1}{x^2})=\lim\limits_{x \to 0}\dfrac{1-x^2}{x^4}=\lim\limits_{x \to 0}\dfrac{1-x^2}{x^4}$ Let $a(x)=\lim\limits_{x \to 0}1 -x^2=1$ Then $\lim\limits_{x \to 0}\dfrac{1-x^2}{x^4}=\lim\limits_{x \to 0}\dfrac{1}{x^4}=\dfrac{1}{0}=\infty$
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