Question

Calcule o limite raiz quadrada de x+6 - 3 ( o 3 não enta em raiz ) sobre x-3 quando x tende a 3 .

Answer 1

$\lim_{x \to \ 3} \frac{ \sqrt{x+6}-3 }{x-3} = \frac{0}{0}$
$\lim_{x \to \ 3} \frac{( \sqrt{x+6}-3 ) ( \sqrt{x+6}+3 )}{(x-3) \sqrt{x+6}+3) }$
$\lim_{x \to \ 3} \frac{ ( \sqrt{x+6} )^{2}- 3^{2} }{(x-3)( \sqrt{x+6}+3 )}$
$\lim_{x \to \ 3} \frac{x+6-9}{(x-3)( \sqrt{x+6}+3 )}$
$\lim_{x \to \ 3} \frac{x-3}{(x-3)( \sqrt{x+6} +3)}$
$\lim_{x \to \ 3} \frac{1}{ \sqrt{x+6}+3 }$
$\lim_{x \to \ 3} \frac{1}{ \sqrt{9}+3 } = \frac{1}{3+3} = \frac{1}{6}$