limitations and infinite

Question

limx→0 (√1+x− √1−x) / (|x|)

Answer 1

For purposes of this editor let a=sqrt(1+x) and b=sqrt(1-x).

The trick here is to multiply the fraction by a+b.

Once you do that the fraction collapses to x/|x| which has no limit as x->0 because it goes to -1 from the left and 1 from the right.