Answer
The attached graph shows the functions at different values of $h$
Work Step by Step
As the mode of $h$ getting smaller and smaller(i.e., approaches to $0$ from either side) from $1$ to $0.1$ our graph becomes good approximation to $f(x)=\frac{1}{2 \sqrt{x}}$.
Actually, if you know the formula of derivative, it's the same.
If $k(x)=\sqrt{x}$
$\frac{dk}{dx}=\frac{1}{2 \sqrt{x}}$ ...(1)
and in the form of limit it becomes
$\frac{dk}{dx}=\lim\limits_{h \to 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}$ ...(2)
If you compare you can see that ultimately both are the same.
