WolframAlpha says limit exists when it doesn't? I was trying to calculate the following limit:

$$
\lim_{(x,y)\to (0,0)} \frac{(x^2+y^2)^2}{x^2+y^4}
$$

and, feeding it into WolframAlpha, I obtain the following answer, stating the limit is $0$:

However, when I try to calculate the limit when $x = 0$ and $y$ approaches 0, the limit is 1...
Is the answer given by WolframAlpha wrong? or am I?

Wolfram Alpha correctly evaluates
$$
\lim_{x\to0}\lim_{y\to0} \frac{(x^2+y^2)^2}{x^2+y^4}= 0
$$
and
$$
\lim_{y\to0}\lim_{x\to0} \frac{(x^2+y^2)^2}{x^2+y^4}= 1.
$$
So one should question the meaning of a limit entered as $(x,y)\to(0,0)$.
