Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 2: Limits and Continuity - Section 2.4 - One-Sided Limits - Exercises 2.4 - Page 75: 45


Yes, see explanations.

Work Step by Step

If $f$ is an odd function of $x$, we have $f(-x)=-f(x)$ and $f$ is symmetric with respect to the origin. Knowing $\lim_{x\to0^+}f(x)=3$, we have $\lim_{x\to0^-}f(x)=\lim_{x\to0^+}f(-x)=-\lim_{x\to0^+}f(x)=-3$ Thus, the answer is Yes.
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