Answer
a. $2$, $1$
b. No.
c. $3$. $3$
d. Yes. $3$
Work Step by Step
Use the figure in the Exercise, given the piecewise function: $f(x)=\begin{cases} 3-x\hspace1cm x\lt2 \\ \frac{x}{2}+1\hspace1cm x\lt2 \end{cases}$
a. $\lim_{x\to2^+}f(x)=2$ and $\lim_{x\to2^-}f(x)=1$
b. No. The limit $\lim_{x\to2}f(x)$ does not exist because $\lim_{x\to2^+}f(x)\ne\lim_{x\to2^-}f(x)$
c. $\lim_{x\to4^-}f(x)=\lim_{x\to4^-}(\frac{x}{2}+1)=\frac{4}{2}+1=3$ and $\lim_{x\to4^+}f(x)=\lim_{x\to4^+}(\frac{x}{2}+1)=\frac{4}{2}+1=3$
d. Yes. The limit $\lim_{x\to4}f(x)=3$
