Find the limit L $($if it exists$).($If an answer does not exist, enter DNE.$)$

$$lim$$x$4$f$($x$)$ where f$($x$)=$

$($x $4)2,$x $44$ x$,$x $>4$

L $=$

If it does not exist, explain why.

The limit does not exist at x $=4$ because the function value is undefined at x $=4.$The limit does not exist at x $=4$ because the function is not continuous at any x value.$$ The limit does not exist at x $=4$ because the function does not approach f$(4)$ as x approaches $4.$The limit does not exist at x $=4$ because the function approaches different values from the left and right side of $4.$The limit exists at x $=4.$