<s>[INST] find the limit of $ \lim_{(x,y) \rightarrow (0,0)}\frac{2xy^3+x^2y^3}{x^4+2y^4}$ find the limit of $$ \lim_{(x,y) \rightarrow (0,0)}\frac{2xy^3+x^2y^3}{x^4+2y^4}$$
I have absolutely no idea how to proceed with that. I would prefer a solution that would involve use of squeeze theorem
 [/INST] Let $y=kx$. So,
$$
\frac{2xy^3+x^2y^3}{x^4 + y^4} = \frac{k^3x^3(2x+x^2)}{x^4(1+k^4)} = \frac{k^3}{1+k^4}(x+2)
$$
and limit depends on $k$; so, it doesn't exists.
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