Question

lim [ 1 - raiz de 1-x / x]
x -> 0

Answer 1

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