Calculus (3rd Edition)

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

Chapter 2 - Limits - 2.6 Trigonometric Limits - Preliminary Questions - Page 76: 1


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Work Step by Step

Since $\lim\limits_{x \to 0}x^2=\lim\limits_{x \to 0}-x^4=0$, then by the Squeeze Theorem, we have $$\lim\limits_{x \to 0}f(x)=0.$$ No, we do not have enough information because in this case the conditions of the Squeeze Theorem are not satisfied. For example, you can see that $\lim\limits_{x \to 1/2}x^2\neq \lim\limits_{x \to 1/2} -x^4$.
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