Define f(0,0)=0 and f(x,y) = x2 +y2-2x2y-4x6y2/(x4+y2)2.
Show for all (x,y) that 4x4y2<=(x4+y2)2 and conclude that f is continuous.
The Attempt at a Solution
Showing the inequality is trivial, but I do not see how I can conclude the function is continuous. I've done some messing around with the form of f, but am not getting anywhere.