Either WolframAlpha or WebAssign is wrong on this, and I can't figure out which. I'm trying to solve lim (x,y) - (0,0) [ (xy^8)/(x^3 + y^12) ]. I've done a variety of exploration (approaching along x-axis, along y-axis, along y=x, along x=y^2, etc.) that tells me the limit might be 0, but I have not done an epsilon-delta proof. According to WebAssign, the limit does not exist. According to WolframAlpha, the limit is 0.

Question

Either WolframAlpha or WebAssign is wrong on this, and I can't figure out which. I'm trying to solve lim (x,y) -> (0,0) [ (xy^8)/(x^3 + y^12) ]. I've done a variety of exploration (approaching along x-axis, along y-axis, along y=x, along x=y^2, etc.) that tells me the limit might be 0, but I have not done an epsilon-delta proof. According to WebAssign, the limit does not exist. According to WolframAlpha, the limit is 0.