I have troubles with such limit
$$ \lim_{(x,y)\rightarrow(0,0)} \frac{x^3}{y^4+2\sin^2{x}}$$
Nothing works, as I approach on any line or curve I get limit equal to $0$.
I try polar coordinates - also nothing, still $0$.
I try to bound it somehow - I get infinity.
However, wolfram tells that there is no limit for the function in $(0,0)$.
If I can get any hint, that would be great.
Call your function $f(x,y)$. Note that $|f(x,y)| \le |f(x,0)|$ and $$ \lim_{x \to 0} f(x,0) = \lim_{x \to 0} \dfrac{x^3}{2\sin^2(x)} = 0$$