Delta/Epsilon Proof for General Cases

[ssayan3]

Hey guys, this isn't a math problem for homework or for a course, but simply for my own interest... This is one that I couldn't crack back in Analysis but that I'd like to get some help on resolving for my own peace of mind:

Prove f(x,y) = xy is continuous at (x,y) in a domain D\subset R. I can do this easily with specific cases of (x,y) but I couldn't ever figure out the general case :-(

 

[LCKurtz]

Try writing xy - ab = (xy - ay) + (ay - ab) and working with that.