Evaluate the limit: limx → 0 (√(1 + x) - (1 - x))/2x

Question

Evaluate the limit: 

\(\lim\limits_{x \to 0} {\frac{\sqrt {1 + x} - \sqrt {1 - x}}{2x}}\)

Answer 1

We need to find the limit of the given equation when x = > 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

Now we can see that the indeterminate form is removed,

So, now we can substitute the value of x as 0, we get