Let $f(x)=\{\begin{array}{cc}3-x,& x<mn>2</mn>\\ \frac{x}{2}& 1,& x>2\end{array}$

Complete parts a through d below.

a$.$ Find $\underset{?}{lim}f(x)$ and $\underset{?}{lim}f(x).$ Select the correct choice below and, if necessary, fill in any answer box$($es$)$ in your choice.

A$.\underset{?}{lim}f(x)=$ and $\underset{?}{lim}f(x)$ does not exist.

$x{2}^{-},x{2}^{}$

$($Simplify your answer.$)$

B$.\underset{x{2}^{}}{lim}f(x)=\underset{x{2}^{-}}{lim}f(x)=$

$($Simplify your answers.$)$

c$.$

$\underset{x{2}^{}}{lim}f(x)=$ and $\underset{x{2}^{-}}{lim}f(x)$ does not exist

$($Simplify your answer.$)$

D$.\underset{x{2}^{}}{lim}f(x)$ and $\underset{x{2}^{-}}{lim}f(x)$ do not exist.

b$.$ Does $\underset{x2}{lim}f(x)$ exist? If so$,$ what is it$?$ If not, why not? Select the correct choice below and, if necessary, fill in any answer box in your choice.

$x2$

A$.$ Yes, $\underset{x2}{lim}f(x)$ exists and equals

$($Simplify your answer.$)$

B$.$ No$,\underset{x2}{lim}f(x)$ does not exist because $f(2)$ is undefined.

C$.$ No$,\underset{x{2}^2}{lim}f(x)$ does not exist because $\underset{x{2}^{}}{lim}f(x)\underset{x{2}^{-}}{lim}f(x).$

c$.$ Find $\underset{x{3}^{}}{lim}f(x)$ and $\underset{x{3}^{-}}{lim}f(x).$ Select the correct choice below and, if necessary, fill in any answer box$($es$)$ in your choice.