The following limit exists, but I can't find its value: $\displaystyle \displaystyle\lim_{(x,y)\to(0,2)}\frac{(y-2)^2\sin(xy)}{x^2+y^2-4y+4}.$
Hope you can help me.
If the limit exists (and I haven't gone so far as to prove that) then it must exist for x, y --> (0, 2) from any way of approaching the point (0, 2). What I would do is to take, say, y = x + 2. Then after you sub y = x + 2 into the limit, you evaluate it for x --> 0.
-Dan