Proving uniform continuity of e^(-x-y) on the first quadrant

[samspotting]

show that f(x,y) = e^(-x-y) is uniformly continuous if x>0 and y>0.

I duno how to start, I know the definition, but if I'm trying to do it the epsilon delta way i don't know how to pick delta and epsilon.

 

[lanedance]

how about noticing that f only varies between zero and 1...

also consider the variable r = x+y, with r>0