Question

Lim raiz quadrada de x+3 - raiz de 3 / x $\lim_{x \to \00} \sqrt{x+3} - \sqrt{3} / x$\

Answer 1

Multiplique pelo conjugado!
$\lim_{x \to 0} \frac{ \sqrt{x+3}- \sqrt{3} }{x} \\ \\ = \lim_{x \to 0} \frac{ \sqrt{x+3}- \sqrt{3} }{x} \frac{ \sqrt{x+3}+ \sqrt{3} }{\sqrt{x+3}+ \sqrt{3}} \\ \\ =\lim_{x \to 0} \frac{(x+3)-(3)}{x(\sqrt{x+3}+ \sqrt{3})} \\ \\ =\lim_{x \to 0} \frac{x}{x(\sqrt{x+3}+ \sqrt{3})} \\ \\ =\lim_{x \to 0} \frac{1}{ \sqrt{x+3}+ \sqrt{3} } = \frac{1}{2 \sqrt{3} }$