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Use Newton's method to find an approximate solution of 2- 9x =x'. Start with x, = 1 and then find x,. ... ロ (Round to four decimal places as needed.) X2 =

Use Newton's method to find an approximate solution of 2- 9x =x'. Start with x, = 1 and then find x,. ... ロ (Round to four decimal places as needed.) X2 =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use Newton's method to find an approximate solution of 2- 9x =x'. Start with x, = 1 and then find x,. ... X2 =0 (Round to four decimal places as needed.)
Transcribed Image Text:Use Newton's method to find an approximate solution of 2- 9x =x'. Start with x, = 1 and then find x,. ... X2 =0 (Round to four decimal places as needed.)
Expert Solution
Step 1

Newton 's method is used to determined the root of real valued function ,  F(x) = 0

The root of the function is determined by the formula                               Xn+1= Xn-(F(x)/F'(x))

F(x)=x3+9x-2=0                                                                        Differentiating with respect to x, we get F'(x)                    F'(x)=3x2+9       

Starting with xo=1

F(xo)=(1)3+9(1)-2                                                                    F(xo)=1+9-2 =8                                                                        F'(xo)=3(1)2+9 = 3+9 =12

x1= xo-(F(xo)/F'(xo))                                                              x1=1-(8/12) = 1-0.6666 = 0.3334

x1= 0.3334

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