Let $f\in C^1$. Prove that for every $x_*$ : $(\nabla \times f)(x_*)=\lim_{\epsilon \rightarrow 0} \frac{1}{\pi \epsilon ^2} \int_{\partial B_\epsilon (x_*)}f(x)dx$
I know that $$ \lim_{\epsilon \rightarrow 0} \frac{1}{\pi \epsilon ^2} \int_{\partial B_\epsilon (x_*)}f(x)dx =\lim_{\epsilon \rightarrow 0} \frac{1}{\pi \epsilon ^2} \int_{B_\epsilon (x_*)}\nabla \times f(x)dx $$
But how can I continue from here? As I obviously can't calculate explicitly the right side of the equation...