Show that applying Newton’s Method to f (x) = x 2 – A produces the iteration of Example 1.6….

Show that applying Newton’s Method to f(x) = x2 − A produces the iteration of Example 1.6.

Example 1.6

Calculate  by using FPI.

An ancient method for determining square roots can be expressed as an FPI. Suppose we want to find the first 10 digits of . Start with the initial guess x0 = 1. This guess is obviously too low; therefore, 2/1 = 2 is too high. In fact, any initial guess 0 <>0 < 2,="" together="" with="">0, form a bracket for . Because of that, it is reasonable to average the two to get a better guess:

 

 

Looking for a Similar Assignment? Let us take care of your classwork while you enjoy your free time! All papers are written from scratch and are 100% Original. Try us today!