Newton-Raphson method is used to compute a root of the equation $x^2 - 13 = 0$ with 3.5 as the initial value. The approximation after one iteration is
follow this one...
This one http://nptel.ac.in/courses/122104019/numerical-analysis/Rathish-kumar/ratish-1/f3node6.html
I have seen this formula, but it looks like Bhagirathi is using some other formula