Question

limite da raiz quadrada de 6-x -2 / raiz quadrada de 3-x -1 quando x tende a 2

Answer 1

$\lim_{x \to \ 2} \frac{ \sqrt{6-x}-2 }{x-2} = \frac{0}{0}$
$\lim_{x \to \ 2} \frac{( \sqrt{6-x}-2 )( \sqrt{6-x}+2 )}{(x-2)( \sqrt{6-x}+2 )}$
$\lim_{x \to \ 2} \frac{ ( \sqrt{6-x} )^{2}- 2^{2} }{(x-2)( \sqrt{6-x}+2 )}$
$\lim_{x \to \ 2} \frac{-x+2}{(x-2)( \sqrt{6-x}+2)}$
$\lim_{x \to \ 2} -\frac{x-2}{(x-2)( \sqrt{6-x}+2)}$
$\lim_{x \to \ 2} -\frac{1}{( \sqrt{6-x}+2)}$
$\lim_{x \to \ 2} - \frac{1}{ \sqrt{6-2}+2 }= \frac{-1}{4}$