Regarding $\lim \limits_{(x,y,z)\to (0,0,0)}\left(\frac{x^2z}{x^2+y^2+16z^2}\right)$--is WolframAlpha incorrect? $$      \lim_{x,y,z\to 0}         {zx^2\over x^2+y^2+16z^2}$$
So I am trying to evaluate this limit..
To me, by using the squeeze theorem, it seems that the answer must be zero.
I trying using the spherical coordinates, which also gives in the same result.
However, WolframAlpha says the limit does not exist.
Could I know whether I am missing something or WolframAlpha is incorrect?(as it happens occasionally)

hint: $0 \leq \dfrac{|zx^2|}{x^2+y^2+16z^2} \leq |z|$
