Question

Calcular o limite da equação

Answer 1

$\lim_{x \to 0} (\frac{\sqrt{x+4}-2}{2x})\\\\ \lim_{x \to 0} [(\frac{\sqrt{x+4}-2}{2x})(\frac{\sqrt{x+4}+2}{\sqrt{x+4}+2})]\\\\ \lim_{x \to 0} [\frac{(\sqrt{x+4}-2)(\sqrt{x+4}+2)}{2x(\sqrt{x+4}+2)}]\\\\ \lim_{x \to 0} [\frac{(\sqrt{x+4})^2-2^2}{2x(\sqrt{x+4}+2)}]\\\\ \lim_{x \to 0} [\frac{x+4-4}{2x(\sqrt{x+4}+2)}]\\\\ \lim_{x \to 0} [\frac{1}{2(\sqrt{x+4}+2)}]\\\\ \lim_{x \to 0} [\frac{1}{2(\sqrt{0+4}+2)}]\\\\ \lim_{x \to 0} (\frac{1}{2.4})\\\\\\ \lim_{x \to 0} (\frac{\sqrt{x+4}-2}{2x})=\frac{1}{8}$