Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 1 - Limits and Continuity - 1.1 Limits (An Intuitive Approach) - Exercises Set 1.1: 17

Answer

False.

Work Step by Step

It's possible that f(a) = L, but $\lim\limits_{x \to a}f(x)$ $\ne$ L. It's enough that $\lim\limits_{x \to a-}f(x)$ $\ne$ L or $\lim\limits_{x \to a+}f(x)$ $\ne$ L. Observe Figure Ex-4, Figure Ex-5, Figure Ex-6 and Figure Ex-7.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.