Answer
$$\frac{1}{4}$$
Work Step by Step
From the figure, we see that
$$\lim _{x \rightarrow 4}\left(\frac{1}{\sqrt{x}-2}-\frac{4}{x-4}\right) =\frac{1}{4}$$
and algebraically, we have
\begin{aligned}
\lim _{x \rightarrow 4}\left(\frac{1}{\sqrt{x}-2}-\frac{4}{x-4}\right) &=\lim _{x \rightarrow 4} \frac{1}{\sqrt{x}+2} \\
&=\frac{1}{\sqrt{4}+2}\\
&=\frac{1}{4}
\end{aligned}
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