Multivariable limit of $\sqrt{x^2+y^2} \sin (\frac{1}{x^2+y^2})$ Find Multivariable limit of $$\lim \limits_{(x,y) \rightarrow (0,0) }\sqrt{x^2+y^2} \sin \left(\frac{1}{x^2+y^2}\right)$$
Limit is obviously zero, but my question is how to simplify it a bit more to make it more obvious?

Notice that
$$
0 \leq \sqrt{x^2+y^2} \left| \sin \left( \frac{1}{x^2+y^2} \right) \right| \leq \sqrt{x^2+y^2}
$$
and by squeezing...
