Wrong Wolfram Alpha result for $\lim_{(x,y)\to(0,0)}\frac{xy^4}{x^4+x^2+y^4}$? 
I'm trying to solve this limit:
  $$
\lim_{(x,y)\to(0,0)}\frac{xy^4}{x^4+x^2+y^4}
$$


Here's my attempt:
$$0 \le |\frac{xy^4}{x^4+x^2+y^4} - 0| = \frac{|x|y^4}{x^4+x^2+y^4},$$ and since $x^4+x^2 \ge0$ then $\frac{y^4}{x^4+x^2+y^4} \le 1$ so 
$$
\frac{|x|y^4}{x^4+x^2+y^4} \le |x|,$$ so 
$$
0 \le \lim_{(x,y)\to(0,0)}|\frac{xy^4}{x^4+x^2+y^4} - 0| \le \lim_{(x,y)\to(0,0)} |x| = 0,
$$ and using the squeeze theorem the limit is $0$. 
But if I input the limit in wolfram alpha, it says that the limit doesn't exist. Here is the link to the limit in Wolfram Alpha.

You can also use polar coordinate by letting $x = r\cos \theta$ and $y = r\sin\theta$ and the limit becomes $$\lim_{r\to 0} \frac{r^5 \cos \theta \sin^4\theta}{r^4\cos^4\theta + r^2\cos^2\theta + r^4\sin^4\theta} = \lim_{r\to 0} r^3\left(\frac{\cos\theta\sin^4\theta}{r^2\cos^4\theta+\cos^2\theta + r^2\sin^4\theta}\right) = 0$$
Today's lesson is : Don't trust Wolframalpha entirely
