The task is to check function uniform continuity in terms of the following set $\{(x,y): x^2+y^2 \geq 2\}$: $$f(x,y)=(x^2+y^2)\cdot \sin\left(\frac{1}{x^2+y^2}\right)$$
Can you help me with this one? I have been solving with only single point to check, however here is the whole set, have no idea what to do with that.
Considering new variable $z = \frac{1}{x^2+y^2}$ we have composition of continuous function with uniformly continuous $f(z)=\frac{\sin z}{z}$ on $0 \leqslant z \leqslant 1$.