Use Newton's method to obtain the third approximation, X2, of the positive fourth root of 5 by calculating the third approximation of the right 0 of f(x)=x²-5. Start with X = 1. The third approximation of the fourth root of 5 determined by calculating the third approximation of the right 0 of f(x)=x²-5, starting with x = 1, is. (Round to four decimal places.)

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 71E
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Use Newton's method to obtain the third approximation, X2, of the positive fourth root of 5 by calculating the third
approximation of the right 0 of f(x) = x4 - 5. Start with X = 1.
The third approximation of the fourth root of 5 determined by calculating the third approximation of the right 0 of
f(x)=x²-5, starting with x₁ = 1, is
4
(Round to four decimal places.)
Transcribed Image Text:Use Newton's method to obtain the third approximation, X2, of the positive fourth root of 5 by calculating the third approximation of the right 0 of f(x) = x4 - 5. Start with X = 1. The third approximation of the fourth root of 5 determined by calculating the third approximation of the right 0 of f(x)=x²-5, starting with x₁ = 1, is 4 (Round to four decimal places.)
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