Hey bkarpuz.

You will have to use the delta epsilon mechanism to show its continuous but basically the limits should exist for all points in the region.

If you can show that the limit point of the function at certain values is a defined quantity then you're done. You should be able to directly use the continuity attributes to say lim x->a f(x,y0) = blah and lim y->b f(x0,y) = blah.