Answer
4
Work Step by Step
Use the "Strategy for Evaluating Limits Algebraically"
1. f is a closed function.
We know by Th.10.1 that it is continuous, that is, L= $\displaystyle \lim_{x\rightarrow a}f(x)$ = $f(a)$,
for all a from the domain of f.
2. Plugging, we see that $x=4$ is NOT in the domain of f.
The form is indeterminate, 0/0 so we try simplifying.
Writing ($x-4$)=$x-2^{2}=(\sqrt{x})^{2}-2^{2}$
= ... difference of squares...
$=(\sqrt{x}+2)(\sqrt{x}-2) ...$we can reduce...
$\displaystyle \lim_{x\rightarrow 4}\frac{(\sqrt{x}+2)(\sqrt{x}-2) }{(\sqrt{x}-2)}=\lim_{x\rightarrow 4}(\sqrt{x}+2)=$
... plug...
$=4$
