Question

lim raiz quadrada de x menos raiz quadrada de 3 sobre x menos 3 quando x tende a 3

Answer 1

$\lim_{x \to \33} \frac{ \sqrt{x} - \sqrt{3} }{x-3} = \lim_{x \to \33} \frac{ \sqrt{x} - \sqrt{3} }{( \sqrt{x}- \sqrt{3})( \sqrt{x} + \sqrt{3}) }= \lim_{x \to \33} \frac{1}{ \sqrt{x} + \sqrt{3} } = \frac{1}{ \sqrt{3}+ \sqrt{3} } = \\ \\ \frac{1}{2 \sqrt{3} } = \frac{1. \sqrt{3} }{2 \sqrt{3}* \sqrt{3} } = \frac{ \sqrt{3} }{6}$