Answer
a. $1$, $1$, $2$
b. Yes. $1$
c. $4$, $4$
d. Yes. $4$
Work Step by Step
Use the figure in the Exercise, given the piecewise function: $f(x)=\begin{cases} 3-x\hspace0.8cm x\lt2 \\2\hspace1.6cmx=2\\ \frac{x}{2}\hspace1.5cm x\gt2 \end{cases}$
a. $\lim_{x\to2^+}f(x)=\frac{2}{2}=1$, $\lim_{x\to2^-}f(x)=3-2=1$, and $f(2)=2$
b. Yes. The limit $\lim_{x\to2}f(x)=1$ because $\lim_{x\to2^+}f(x)=\lim_{x\to2^-}f(x)$
c. $\lim_{x\to-1^-}f(x)=\lim_{x\to-1^-}(3-x)=3+1=4$ and $\lim_{x\to-1^+}f(x)=\lim_{x\to-1^+}(3-x)=3+1=4$
d. Yes. The limit $\lim_{x\to-1}f(x)=4$ because $\lim_{x\to-1^+}f(x)=\lim_{x\to-1^-}f(x)$
