Evaluate the following limits: \[\underset{x\to 0}{\mathop{\lim }}\,\frac{2x}{\sqrt{a+x}-\sqrt{a-x}}\]

We need to find the limit of the given equation when \[x\text{ }=>\text{ }0\]

Now let us substitute the value of x as \[0\], we get an indeterminate form of \[0/0\].

Let us rationalizing the given equation, we get