Question

lim(1-√x)/x-1 quando o x=>1

Answer 1

Resposta:

$\boxed{\mathsf{- \frac{1}{2}}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{\lim_{x \to 1} \frac{1 - \sqrt{x}}{x - 1} =} \\\\\\ \mathsf{\lim_{x \to 1} \frac{(1 - \sqrt{x})}{(x - 1)} \cdot \frac{(1 + \sqrt{x})}{(1 + \sqrt{x})}=} \\\\\\ \mathsf{\lim_{x \to 1} \frac{1 - x}{(x - 1)(1 + \sqrt{x})}=} \\\\\\ \mathsf{\lim_{x \to 1} \frac{- (x - 1)}{(x - 1)(1 + \sqrt{x})}=}$

$\\ \displaystyle \mathsf{\lim_{x \to 1} \frac{- \cancel{\mathsf{(x - 1)}}}{\cancel{\mathsf{(x - 1)}}(1 + \sqrt{x})}=} \\\\\\ \mathsf{\lim_{x \to 1} \frac{- 1}{(1 + \sqrt{x})}=} \\\\\\ \mathsf{\frac{- 1}{1 + 1} =} \\\\\\ \boxed{\boxed{\mathsf{- \frac{1}{2}}}}$