Evaluating $\lim_{(x,y)\to(0,0)}\dfrac{x^2+y^2}{x^4+y^4}$ 
Evaluate the limit: $\displaystyle\lim_{(x,y)\to(0,0)}\dfrac{x^2+y^2}{x^4+y^4}$

To solve this, I converted it to polar coordinate and got: $\displaystyle\lim _{r\to0}\left(\frac{1}{r^2(\sin^4\theta+cos^4\theta)}\right)=\infty$
But after putting this on WolframAlpha, it tells me that this limit does not exist.
Who is wrong here?


We can also see that :
$$\dfrac{x^2 + y^2}{x^4 + y^4} \geq \dfrac{x^2 + y^2}{(x^2 + y^2)^2} = \dfrac{1}{x^2 + y^2} \underset{(x, y) \to (0, 0)}{\to} +\infty$$
