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 \(\lim\limits_{\text x \to 0}\cfrac{\sqrt{1+\text x}-\sqrt{1-\text x}}{2\text x} \) = \(\cfrac1{1+1}=\cfrac12\)