Answer
$$\lim_{x \to 4}\sqrt{x}$$For the proof by using the $\epsilon - \delta$ definition, see below.
Work Step by Step
$$\lim_{x \to 4} (\sqrt{x})=\sqrt{4}=2$$Now, we want to prove this limit by using $\epsilon - \delta$ definition; that is, we must show that for each $\epsilon >0$, there exists a $\delta >0$ such that $|\sqrt{x}-2|< \epsilon$ whenever $|x-4|< \delta$.
Now, we have$$|\sqrt{x}-2|=|\frac{1}{\sqrt{x}+2}||x-4|.$$For all $x$ in the interval $(3,5)$
