Question

Limites!

$\lim_{x\ \to \ 9} \frac{ \sqrt{x} - 3}{x-9}$

Answer 1

 Boa noite, Elizeu!

 Ao substituíres x por 9, indeterminação! Por isso, devemos racionalizar o numerador.
 
 Segue,

$\lim_{x\to9}\frac{\sqrt{x}-3}{x-9}\;\;\times\frac{\sqrt{x}+3}{\sqrt{x}+3}=\\\\\\\lim_{x\to9}\frac{x-9}{(x-9)(\sqrt{x}+3)}=\\\\\\\lim_{x\to9}\frac{1}{\sqrt{x}+3}=\\\\\\\frac{1}{\sqrt{9}+3}=\\\\\\\frac{1}{3+3}=\\\\\\\boxed{\frac{1}{6}}$