Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 4 - Applications of the Derivative - 4.7 Newton's Method - Preliminary Questions - Page 219: 2


every term equals to $x_0 $

Work Step by Step

Since $$ x_{n+1}=x_{n}-\frac{f\left(x_{n}\right)}{f^{\prime}\left(x_{n}\right)}$$ Then for $x_0= 0$ $$x_{1}=x_{0}-\frac{f\left(x_{0}\right)}{f^{\prime}\left(x_{0}\right)}=x_{0}-0=x_{0} $$ Hence, every term equals to $x_0 $.
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