Question : For f(x,y)=xy, show that f(x,y) is continuous everywhere.
i.e. for every point (a,b) in the plane and for every epsilon>0, find delta>0 depending on a,b and epsilon such that whenever
0<|(x,y)-(a,b)|<delta, |f(x,y)-f(a,b)|<epsilon
How to find an epsilon in terms of delta? I am troubled in expressing epsilon as a function of delta.
Many thanks.