Newton's Method: Quiz
Problem 1
Using Newton's Method, estimate the solution to x2 − 77 = 0. Give your answer correct to 5 decimal places.
Answers, problem 1
The derivative is 2x. Newton's Method gives us xn+1 = xn – (xn2 – 77)/(2 xn) = xn/2 + 77/(2 xn).
Pick an arbitrary first point, say x0 = 7.
x1 = 7/2 + 77/14 = 9
x2 = 9/2 + 77/18 = 8.77778
x3 = 8.77778/2 + 77/17.55556 = 8.77496
More iterations give the same answer, so we estimate the solution to be 8.77496.