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