Question

limx→4 Raiz quadrada de x - 2/x^2 - 4x

Answer 1

$\lim_{x\to4}\frac{\sqrt{x}-2}{x^2-4x}$

$\lim_{x\to4}\frac{\sqrt{x}-2}{x^2-4x}*\frac{\sqrt{x}+2}{\sqrt{x}+2}$

$\lim_{x\to4}\frac{x-4}{x(x-4)(\sqrt{x}+2)}$

$\lim_{x\to4}\frac{1}{x(\sqrt{x}+2)}$

$\boxed{\boxed{\lim_{x\to4}\frac{\sqrt{x}-2}{x^2-4x}=\frac{1}{16}}}$