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

Answer

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