更新1:
e.g. f(x,y) = xy^2 / (x^2+y^2) When taking limit along y-axis or x-axis, it equals 0. When taking limit along y = mx, it also equals 0. But when taking limit along x=ay^2, it doesn't equal 0. So the limit of f(x,y) doesn't exist.
更新2:
I just imagine when the limit is taken along x=ay^3, x=ay^4, ......, the limit seems to exist. But there may have a path x=ay^10 along which the limit doesn't exist.
