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 74: 8


a. See graph. b. $0$, $0$ c. Yes.

Work Step by Step

We are given the piecewise function: $f(x)=\begin{cases} 1-x^2\hspace1cm x\ne1 \\ 2\hspace2cm x=1 \end{cases}$ a. See graph. b. $\lim_{x\to1^+}f(x)=\lim_{x\to1^+}(1-x^2)=0$ and $\lim_{x\to1^-}f(x)=\lim_{x\to1^1}(1-x^2)=0$ c. Yes. The limit $\lim_{x\to1}f(x)=0$ because the left and right side limits are equal.
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.