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Compute: $\displaystyle\lim_{x\rightarrow 2}\frac{\sqrt{x+1}-\sqrt{ 1-x}}{x}$

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    I'm not sure that the problem was to compute the limit when x --> 2...2012-10-25

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I assume you are interested in $\lim_{x \to 0} \dfrac{\sqrt{1+x} - \sqrt{1-x}}x$ Multiply and divide by $\sqrt{1+x} + \sqrt{1-x}$ to get $\dfrac{\sqrt{1+x} - \sqrt{1-x}}x \times \dfrac{\sqrt{1+x} + \sqrt{1-x}}{\sqrt{1+x} + \sqrt{1-x}} = \dfrac{(1+x)-(1-x)}{x(\sqrt{1+x} + \sqrt{1-x})} = \dfrac{2x}{x(\sqrt{1+x} + \sqrt{1-x})}\\ = \dfrac2{\sqrt{1+x} + \sqrt{1-x}}$ Now can you finish it off?

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Just evaluate the function at $x = 2$.