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

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