Answer
See answer below.
Work Step by Step
When the function $f$ is continuous at $ (x_0,y_0)$ then
$\lim\limits_{(x,y) \to (x_0,y_0) }f(x,y)=3$
This implies that the limit is equal to the function value and the function is continuous at that point.
When the function $f$ is not continuous at $ (x_0,y_0)$ then the limit may or may not be equal to the function value, that is, $3$. It can be possible only when it is a removable discontinuity; in that case, the limit will not exist.
