Question

Limites indefinidos com Raiz.

Answer 1

$\lim_{x \to 3} \frac{ \sqrt{x+6}-x }{(x^{3}-3 x^{2} )}. \frac{ \sqrt{x+6}+x }{ \sqrt{x+6}+x }=> \lim_{x \to 3} \frac{( \sqrt{x+6})^{2}-x^{2}}{(x^{3}-3x^{2})( \sqrt{x+6}+x )}=>$

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

$\lim_{x \to 3} \frac{-x-2}{x^{2}( \sqrt{x+6}+x )}=> \lim_{x \to 3} \frac{-3-2}{3^{2}( \sqrt{3+6}+3 )}=> -\frac{5}{54}$