Question

Limite indefinido

$\lim_{x \to \inft1} \sqrt{ \frac{ \sqrt{x} -1}{x-1} }$

Answer 1

$\lim_{n \to\11} \sqrt{ \frac{ \sqrt{x}-1 }{x-1} } = \lim_{n \to \11} \sqrt{ \frac{ \sqrt{x}-1 }{( \sqrt{x}+1)( \sqrt{x}-1) } } = \\ \\ \lim_{n \to \11} \sqrt{ \frac{1}{ \sqrt{x}+1 } }= \sqrt{ \frac{1}{ \sqrt{1}+1 } } = \sqrt{ \frac{1}{2} } = \frac{1}{ \sqrt{2} } = \frac{ \sqrt{2} }{2}$