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

1.	Evaluate:\(\lim\limits_{x \to 1}\frac{\sqrt {1+x}-\sqrt {1-x}}{1+x}\)
Answer» \(\lim\limits_{x \to 1}\frac{\sqrt {1+x}-\sqrt {1-x}}{1+x}\) \(=\lim\limits_{x \to 1}\frac{\sqrt {1+1}-\sqrt {1-1}}{1+1}\) \(=\frac{\sqrt 2-0}{2}\) \(=\frac{\sqrt 2}{2}\) \(=\frac{1}{\sqrt 2}\)

Answer»

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

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

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

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

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

Discussion

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