Need to find $\lim_{x\to4}\bigl((1/\sqrt x)-(1/2)\bigr)/(x-4)$ This one is frustrating $$\lim\limits_{x\to 4} \frac{(1 / \sqrt{x}) - \frac12}{x-4}$$

$\lim\limits_{x\to 4} \frac{(1 / \sqrt{x}) - \frac12}{x-4}$.
We substition $\sqrt {x}=t$, hance we:
If $ x\longrightarrow 4\Rightarrow t\longrightarrow 2. $
From here for the given limits have:
$\lim\limits_{x\to 4} \frac{(1 / \sqrt{x}) - \frac12}{x-4}$=$\lim\limits_{t\to 2} \frac{\frac{1}{t} - \frac12}{t^2-4}$=$\lim\limits_{t\to 2} \frac{\frac{2-t}{2t}}{t^2-4}$=$\lim\limits_{t\to 2} \frac{2-t}{2t(t-2)(t+2)}$=$-\lim\limits_{t\to 2} \frac{t-2}{2t(t-2)(t+2)}$=$-\lim\limits_{t\to 2} \frac{1}{2t(t+2)}$=$-\frac{1}{16}$
