Question

Lim /x_1 x^2-1/raiz de x-1

Answer 1

diferença dos quadrados
$\boxed{\boxed{a^2-b^2=(a+b)*(a-b)}}$


aplicando isso:

$\lim_{x \to 1} \frac{\sqrt{x^2-1}}{\sqrt{x-1}} \\\\ \lim_{x \to 1} \sqrt{ \frac{x^2-1}{x-1} }\\\\ \lim_{x \to 1} \sqrt{ \frac{(x-1)*(x+1)}{x-1} }\\\\ \lim_{x \to 1} \sqrt{x+1}= \sqrt[]{1+1} =\sqrt{2}$