Answer
(a) $L\approx 5.545$
(b) $f$ is increasing
Work Step by Step
We are given the function:
$f(x)=\dfrac{2^x-8}{x-3}$
(a) Graph the function and zoom to estimate $L=\displaystyle \lim_{x\rightarrow 3} f(x)$:
$L=\displaystyle \lim_{x\rightarrow 3} \dfrac{2^x-8}{x-3}\approx 5.545$
(b) $f(2.999999)\leq L\leq f(3.00001)$
because the function $f$ is increasing on its domain, so for $x_1
