This is Ana's definition of the derivative:
$f'(a)=\lim\limits_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}$
That means $f(x)=\sqrt{3-x}\text{ and }a=0.$
Find $f^\prime(x)$ and then the limit will equal $f^\prime(0)$.

Or you could multiply the numerator and denominator by the conjugate of the numerator.

Evaluate. The denominator will not equal zero so the limit and the actual value agree at $x = 2$.

Rewrite the absolute value as a piecewise function but, since $x → 2^+$, only consider the piece in which $x > 2$.

Think about what the graph of $y = e^{−x}$ looks like. What does it look like all the way to the right, as $x → ∞$? How does the $+1$ affect the graph?