#### Answer

$\lim\limits_{x \to 9}\frac{\sqrt x - 3}{x-9} = \frac{1}{6} = 0.16$

#### Work Step by Step

$\frac{\sqrt x - 3}{x-9} = \frac{\sqrt x - 3}{(\sqrt x)^{2}-3^{2}} = \frac{\sqrt x - 3}{(\sqrt x-3)(\sqrt x+3)} = \frac{1}{(\sqrt x+3)}$
Now,
$\lim\limits_{x \to 9}\frac{\sqrt x - 3}{x-9} = \frac{1}{(\sqrt x+3)} = \frac{1}{3+3} = \frac{1}{6} = 0.16$