I have some problem to understand the definition of a continuous function in a point.
I have $f(x) = \sqrt{x}$ and I want to check the continuity of the function above in the point $x_0 = 0$ or for all the $x_0 \ge 0$.
Using the relation between $|f(x) -f(x_0)|< \epsilon$ and $|x - x_0| < \delta$ that states: $\forall\epsilon \in \Bbb R, \exists\delta\in\Bbb R : \forall x \in domain \mathcal (f): |x-x_0| < \delta \Rightarrow |f(x)-f(x_0)| < \epsilon$, how can I check continuity at a point?
Thanks