\(\lim _{x \rightarrow 4}\left[\frac{x-4}{\sqrt{x}-2}\right]=\lim _{x \rightarrow 4}\left[\frac{x-4}{\sqrt{x}-2} \cdot \frac{\sqrt{x}+2}{\sqrt{x}+2...

\(\lim _{x \rightarrow 4}\left[\frac{x-4}{\sqrt{x}-2}\right]=\lim _{x \rightarrow 4}\left[\frac{x-4}{\sqrt{x}-2} \cdot \frac{\sqrt{x}+2}{\sqrt{x}+2}\right]=\lim _{x \rightarrow 4}\left[\frac{(x-4)(\sqrt{x}+2)}{x-4}\right]=\lim _{x \rightarrow 4}[\sqrt{x}+2]=\sqrt{4}+2=4\)