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.

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.