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 2.5 - Continuity - Exercises 2.5 - Page 84: 12

Answer

Discontinuities at $ x=1$ (nonremovable) and $ x=2$ (removable).

Work Step by Step

We are given the function $ f(x)$. The discontinuity at $ x=1$ is a jump discontinuity and therefore cannot be removed. The discontinuity at $ x=2$ can be removed by defining $ f(2)=1$ (that would make the limit as $ x $ goes to $2$ equal to $ f(2)$, since the limit exists).
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.