Question

lim (raiz de x+1) - 3 / x - 8 com x tendendo a 8

Answer 1

$\lim_{x \to 8} \left( \frac{ \sqrt{x+1}-3 }{x-8} \right)= \frac{0}{0}$

multiplicando pelo conjugado do numerador

$\lim_{x \to 8} \left( \frac{ \sqrt{x+1}-3 }{x-8} \right) * \left( \frac{ \sqrt{x+1}+3 }{ \sqrt{x+1}+3} \right)\\\\ \lim_{x \to 8} \frac{( \sqrt{x+1})^2-(3)^2 }{(x-8)* (\sqrt{x+1}+3)}\\\\\lim_{x \to 8} \frac{(x+1) -9}{(x-8)* (\sqrt{x+1}+3)}\\\\\\= \lim_{x \to 8} \frac{(x-8) }{(x-8)* (\sqrt{x+1}+3)}= \frac{1}{\sqrt{x+1}+3} = \frac{1}{\sqrt{8+1}+3}= \frac{1}{3+3}= \frac{1}{6}$