Solved.
Thanks
Ok, for any $\displaystyle \varepsilon>0$ you can find $\displaystyle r_0>0$ such that $\displaystyle \inf\{f(x):x\in B(x,r)\}\geq f(x_0)-\varepsilon$ and $\displaystyle \sup\{f(x):x\in B(x,r)\}\leq f(x_0)+\varepsilon$ for each $\displaystyle r<r_0$. This allows you to get upper and lower estimates of the limit as close to $\displaystyle f(x_0)$ as you want.