Answer
a. See graph.
b. $1$, $1$
c. Yes. $1$
Work Step by Step
We are given the piecewise function:
$f(x)=\begin{cases} x^3\hspace1cm x\ne1 \\ 0\hspace1cm x=1 \end{cases}$
a. See graph.
b. $\lim_{x\to1^-}f(x)=\lim_{x\to1^-}x^3=1$ and $\lim_{x\to1^+}f(x)=\lim_{x\to1^+}x^3=1$
c. Yes. The limit $\lim_{x\to1}f(x)=1$ because $\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=1$
