$\displaystyle lim_{(x,y) \to (0,0)} \frac{4x^2+3y^2 +x^3y^3}{x^2+y^2+x^4y^4}$

I know can't use L'Hospitals rule anymore and I don't see a way of factoring to clean it up. My intuition tells me the limit does not exist.

I just need help trying to prove it, the question specifically says "do not attempt a precise justification"