Finding Multivariable limits using polar coordinates How do I find the limit of this multivariable function as it goes to zero using polar coordinates?
$$ \frac{\sin (x^2 + y^2)}{(x^2 + y^2)^2}
$$

Use 
\begin{align}
 x &= r \cos \theta \\
 y &= r \sin \theta
\end{align}
So $x^2 + y^2 = r^2$ hence
\begin{equation}
 \frac{\sin (x^2 + y^2)}{(x^2 + y^2)^2}
 =
 \frac{\sin r^2}{r^4}
\end{equation}
Using L'Hopital twice, we get
\begin{equation}
\frac{\sin r^2}{r^4}
\sim
\frac{2\cos\left(r^2\right)-4r^2\sin\left(r^2\right)}{12r^2}
\rightarrow 
+\infty
\end{equation}
