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

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

lim(x→0) (2x)/√(a +x) - √(a - x)

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

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 $\lim\limits_{\text x \to 0}\cfrac{2\text x}{\sqrt{a+\text x}-\sqrt{a-\text x}}$ = $\sqrt a+\sqrt a=2\sqrt a$