Tricky limit involving sine I'm trying to evaluate
$$\text{lim}_{(x,y) \rightarrow (0,0)} \frac{x^4 + \text{sin}^2(y^2)}{x^4+y^4}.$$
I'm pretty sure that the limit exists and is $1$; at the very least, you get that if you approach $(0,0)$ along the lines $x=0$ and $y=0$ and $x=y$.  But I can't seem to figure out how to to show that the limit is $1$.  Thanks!

Hint: Taylor series of $\sin^2(y^2)$ at $y=0$ gives

$$ \sin^2(y^2) \sim y^4  . $$

