Question

Prove that root function is a continuous function.

Answer 1

Let \(\delta=\varepsilon\). Choose \(c\in\mathbb{R}\). Then for every \(\varepsilon>0\), we have that \(|\sqrt x-\sqrt c|\leqslant|x-c|<\delta=\varepsilon\), for all \(x\in\mathbb{R}\). Hence, \(\sqrt\cdot\) is a continuous function.

Answer 2

thanx!