Use the graph of the function $f$ shown to estimate the indicated limits and the function value. Complete parts $($A$)$ through $($D$).$

A$.\underset{x{0}^{+}}{lim}f(x)=2($Type an integer.$)$

B$.$ The limit does not exist.

$($B$)$ Find the limit $\underset{x{0}^{-}}{lim}f(x).$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\underset{x{0}^{-}}{lim}f(x)=,($Type an integer.$)$

B$.$ The limit does not exist.