Continuity for 2D Functions

A function $f(x,y)$ is called continuous at a point $(x_0,y_0)$ if:

1. $f(x,y)$ is defined at $(x_0,y_0)$
2. ${\lim }_{(x,y)\to (x_0,y_0)}f(x,y)$ exists
3. ${\lim }_{(x,y)\to (x_0,y_0)}=f(x_0,y_0)$