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 2.2 - Limit of a Function and Limit Laws - Exercises 2.2 - Page 56: 8


Although $ f(x)$ is defined in $[-1,1]$ which means $ f(0)$ is defined, it does not mean that the limit of $ f(x)$ exists at $ x=0$.

Work Step by Step

For instance, there could be a jump discontinuity at $x=0$, and even though the value there is defined, the limits from the left and right side may not match.
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