Let $f(x)=\{\begin{array}{cc}5-x,& x<mn>4</mn>\\ \frac{x}{2}& 2,& x>4\end{array}$

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$.\underset{x{4}^{-}}{lim}f(x)=$ and $\underset{x{4}^{}}{lim}f(x)$ does not exist.

$($Simplify your answer.$)$

B$.\underset{x{4}^{}}{lim}f(x)=\underset{x{4}^{-}}{lim}f(x)=$

$$

$($Simplify your answers.$)$

C$.\underset{x{4}^{}}{lim}f(x)=$ and $\underset{x{4}^{-}}{lim}f(x)$ does not exist.

$($Simplify your answer.$)$

D$.\underset{x{4}^{}}{lim}f(x)$ and $\underset{x{4}^{-}}{lim}f(x)$ do not exist.