find limit of a multivariable function I have to show continuity at $(0,0)$ of $f(x,y)=\frac{\sin(x^2) + \sin(y^2)}{\sqrt{x^2 +y^2}}$ for $(x,y)\ne(0,0)$ and $f(0,0)=0$.
I tried to find the limit using polar coordinates
$ \frac{\sin(r^2\cos^2 α) + \sin(r^2\sin^2 α)}{r} $
but it's still $\frac00$ 

\begin{align*}T&:=\frac{\sin \ x^2+\sin\ y^2}{\sqrt{x^2+y^2}}
 \\&=\frac{\sin \ x^2 }{x^2}\frac{x^2}{
 \sqrt{x^2+y^2}} +
 \frac{\sin\ y^2}{y^2}\frac{y^2}{
 \sqrt{x^2+y^2}}
\\&\leq \frac{\sin \ x^2 }{x^2}\frac{x^2 +y^2}{
 \sqrt{x^2+y^2}} +
 \frac{\sin\ y^2}{y^2}\frac{x^2+y^2}{
 \sqrt{x^2+y^2}} \rightarrow 0 \end{align*}
When $x,\ y\rightarrow 0$, then $T\geq 0$ so that $T$ has a limit
$0$ 
