To approximate the reciprocal of a number a without using division, we can apply Newtons method to
Question:
To approximate the reciprocal of a number a without using division, we can apply Newton’s method to the function f(x) = 1/x - a.
a. Verify that Newton’s method gives the formula xn + 1 = (2 - axn)xn.
b. Apply Newton’s method with a = 7 using a starting value of your choice. Compute an approximation with eight digits of accuracy. What number does Newton’s method approximate in this case?
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Related Book For 
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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