We can say that as the , or .

If, intuitively speaking, by going close enough to (a,b) we can get f(a,b) as close as we like to L.

f(x,y) is said to be continuous at (a,b) if .

Just as with one variable limits from below and above may be different, with two variables we may get various limits coming in from different paths.

##### Example

Consider coming in to (0,0) along the line y=mx (m fixed). Along this line we have:

Thus along y=mx,

If we come in along the line ,

.