Evaluate a limit in terms of derivative If $f$ is differentiable at $x = a$, with $a &gt; 0$, evaluate the following limit in terms of $f'(a)$

$$\lim_{x \to a}\frac{f(x) - f(a)}{\sqrt{x} - \sqrt{a}}$$
HINT

Use that

$$\lim_{x \to a}\frac{f(x) - f(a)}{\sqrt{x} - \sqrt{a}}=\lim_{x \to a}\left(\frac{f(x) - f(a)}{x-a}\cdot \frac{x-a}{\sqrt{x} - \sqrt{a}}\right)$$
Take the derivative (l’hopital rule) to get: ( since it is zero divided by zero)

$f’(x)(2)x^{0.5}$

This gives 

$f’(a)(2)a^{0.5}$