$(5$ points$)$ Given $f(x)=\{\begin{array}{ccc}4-x& if& x<mn>3</mn>\\ 5& if& x=3\\ ln(x-3)& if& x>3\end{array}$

$($a$)$ Find each of the following or write DNE $($does not exist$).$ Include infinite limits$.$

$\underset{x{3}^{-}}{lim}f(x)=$

$$

$\underset{x{3}^{}}{lim}f(x)=$

$$

$f(3)=$

$($b$)$ Based on the results from part $($a$)$ we can say that $f$ is $($choose one$)$

$($i$)$ continuous at $3$

$($ii$)$ left$-$continuous at $3$

$($iii$)$ right$-$continuous at $3$

$($iv$)$ none of these

$($c$)$ Based on the results from part $($a$)$ we can say that at $x=3,f$ has $($choose one$)$

$($i$)$ a jump discontinuity

$($ii$)$ a removable discontinuity

$($iii$)$ an infinite discontinuity

$($iv$)$ none of these