Let f(x,y) be defined by f(x,y) = [x2y2]/[x2y2 + (x-y)2] a) Find the domain of the function f. b) show that (0,0) is a boundary point of the domain of f c) Compute the following limit if it exists: lim (x,y) ---> (0,0) f(x,y) 3. The attempt at a solution a) I first change the value (x-y)2 to (x2+y2-2xy). I then looked at it logically and said that the denominator obviously can't be equal to zero. And if I rewrote it to look like x2y2+x2+y2-2xy, I can see that 2xy is the only term that is not squared, which means it is the only term capable of being negative. So I wrote that x2y2+x2+y2 > 2xy That is it for the domain. Is my logic correct here? b) I believe I somewhat have an understanding of boundary points. Basically it means that for a neighborhood of x (an open set, U, that x is contained in), at least one point of U will be contained inside and outside of A. Correct? This being said, I'm still not really sure how to do this part of the problem. The domain at (0,0) is undefined because x2y2+x2+y2 = 2xy, causing you to divide by zero. Is this in a sense proving already that it is a boundary point? Because x=0 and y=0 by themselves are contained in the domain but when both are, they are not. Am I completely wrong here in that assumption? c) I'm really not sure how to go about trying to calculate this limit. Limits are not my specialty. I can't think of a path that doesn't lead to 0, but that isn't proof enough to say that the limit definitively exists. Some help would be greatly appreciated! Thank you!