Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.8 - Newton''s Method - 4.8 Exercises: 8

Answer

$x_{3} = -1.29172$

Work Step by Step

$f(x) = x^7 + 4$ $f'(x) = 7x^6$ $x_{n+1}=x_{n}-\frac{x_n^7+4}{7x_n^6}$ $x_{1} = -1$ $x_{2} = -1 - \frac{-1^7 + 4}{7(-1^6)}$ $x_{2} = -1 - \frac{3}{7}$ $x_{2} = -1.42857$ $x_{3} = -1.42857 - \frac{-1.42857^7 + 4}{7(-1.42857)^6}$ $x_{3} = -1.42857 + 0.136853$ $x_{3} = -1.29172$
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