How far have you gotten with part a)? You should find that you derive a method for approximating square roots known to the Babylonians, although their method of derivation is somewhat simpler, but ingenious.
(a) Set up and simplify the iterative formula for Newton's method to solve for
solutions to the equation
x^2 - a = 0
(b) For a = 11 find and verify an interval of positive values of the type [n; n + 1]
that contains a solution and use the left hand side of the interval for x1 to find x2
and x3 as fractions.
Please Explain with steps. Thank You.