Evaluate lim(x→1)[(√1+x)-(√1-x)]/1+x

Question

Evaluate:

\(\lim\limits_{x \to 1}\frac{\sqrt {1+x}-\sqrt {1-x}}{1+x}\)

Answer 1

\(\lim\limits_{x \to 1}\frac{\sqrt {1+x}-\sqrt {1-x}}{1+x}\) 

\(=\lim\limits_{x \to 1}\frac{\sqrt {1+1}-\sqrt {1-1}}{1+1}\) 

\(=\frac{\sqrt 2-0}{2}\)

\(=\frac{\sqrt 2}{2}\) 

\(=\frac{1}{\sqrt 2}\)