# Evaluate the following limit : lim(x→0) (√(1 + x) - √(1 - x))/2x

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Evaluate the following limit : $\lim\limits_{\text x \to 0}\cfrac{\sqrt{1+\text x}-\sqrt{1-\text x}}{2\text x}$

im(x→0) (√(1 + x) - √(1 - x))/2x

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Given $\lim\limits_{\text x \to 0}\cfrac{\sqrt{1+\text x}-\sqrt{1-\text x}}{2\text x}$

To find: the limit of the given equation when x tends to 0

Substituting x as 0 we get an indeterminant form of $\cfrac00$

Rationalizing the given equation

Formula: (a + b) (a - b) = a2 - b2

Now we can see that the indeterminant form is removed, so substituting x as 0

We get $\lim\limits_{\text x \to 0}\cfrac{\sqrt{1+\text x}-\sqrt{1-\text x}}{2\text x}$ = $\cfrac1{1+1}=\cfrac12$