Let a > 0 be given and suppose we want to approximate a using Newtons method. a.

Question:

Let a > 0 be given and suppose we want to approximate √a using Newton’s method. 

a. Explain why the square root problem is equivalent to finding the positive root of f(x) = x2 - a.

for n = 0, 1, 2, . . .. Хп. Хл+1 Xn

b. Show that Newton’s method applied to this function takes the form (sometimes called the Babylonian method).

c. How would you choose initial approximations to approximate √13 and √73?

d. Approximate √13 and √73 with at least 10 significant digits.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Question Posted: