<s>[INST] Find $\lim_{(x,y) \to (0,0)} \frac{\sin{(x^3 + y^5)}}{x^2 + y^4}$. Prove your result. Find $\lim_{(x,y) \to (0,0)} \frac{\sin{(x^3 + y^5)}}{x^2 + y^4}$.  Prove your result.
I've attempted to apply the Squeeze Theorem as such:
$\frac{-1}{x^2 + y^4} \leq \frac{\sin{(x^3 + y^5)}}{x^2 + y^4} \leq  \frac{1}{x^2 + y^4}$.  Clearly, though, the leftmost and rightmost functions of this inequality tend to $\infty$  as $(x,y) \to 0$, so this result does not help.
 [/INST] Here's another hint/warm-up problem:
$$\lim_{(x,y)\to (0,0)}\frac{x^6+y^5}{x^4+y^4}.$$
</s>