Expert: David Hemmer - 10/28/2009

Question
Can you please help me with an epsilon delta proof of two variables?
I need to prove the limit of cos(xy) as f(x,y) --> (1,pi/2)


Answer
Well the limit is clearly 0, which you get by substituting since cos(xy) is continuous. So now suppose epsilon>0 is given. You need to choose a delta so that for any (a,b) in a delta ball around (1, pi/2) that |cos(ab)|<epsilon.

I'd suggest first finding an epsilon that works in the proof that the limit of cos(y) as y-> pi/2 is equal to zero. Once you have this it's easy enough to pick a new epsilon that works for cos(ab). Let me know if you need more hints.