\begin{equation}f(x)=\left\{\begin{array}{ll}{3-x,} & {x<2} \\ {\frac{x}{2}+1,} & {x>2}.\end{array}\right.\end{equation}
\begin{equation}
\begin{array}{l}{\text { a. Find } \lim _{x \rightarrow 2^{+}} f(x) \text { and } \lim _{x \rightarrow 2^{-}} f(x).} \\ {\text { b. Does } \lim _{x \rightarrow 2^{+}} f(x) \text { exist? If so, what is it? If not, why not? }} \\ {\text { c. Find } \lim _{x \rightarrow 4^{-}} f(x) \text { and } \lim _{x \rightarrow 4^{+}} f(x).} \\ {\text { d. Does } \lim _{x \rightarrow 4} f(x) \text { exist? If so, what is it? If not, why not? }}\end{array}
\end{equation}