Limits and Continuity of Bivariate Functions

Just like single-variable functions, Limit and continuity also apply to functions of two (or more!) variables, in a similar manner.

Limits §

Let $f(x,y)$ be a function of two variables.

The limit of $f(x,y)$ as $(x,y)$ approaches $(x0,y0)$ is L, written as:

$$\underset{(x,y)\to (x_0,y_0)}{\lim }f(x,y)=L$$

The same rules of limits and limit laws apply.