Approximating square roots Let a 7 0 be given and suppose
Chapter 4, Problem 42(choose chapter or problem)
Approximating square roots Let a 7 0 be given and suppose we want to approximate 1a using Newtons method. a. Explain why the square root problem is equivalent to finding the positive root of f 1x2 = x2 - a. b. Show that Newtons method applied to this function takes the form (sometimes called the Babylonian method) xn + 1 = 1 2 axn + a xn b, for n = 0, 1, 2, c. c. How would you choose initial approximations to approximate 113 and 173? d. Approximate 113 and 173 with at least 10 significant digits.
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