Consider the function f(x) = 3x³ + 2x – 1 and the equation f(x) = 0. (d) Use Newton's method to approximate r to eight correct decimal places (startingwith xo = 0.5). Report the approximation xe, number of steps needed, and thebackward error |f(xc)|.(e) Modify the code on Newton's method in order to solve the equation using Halley'smethod, an iterative process given by2f(xk) f'(xk)Xk+1H(xk) = Xk2(f'(x))? – f(Xx)f"(xx) *0.5). ReportApproximate r to eight correct decimal places (starting with xo =the approximation xe, number of steps needed, and the backward error |f (xc)]-

Given :- Consider the function f x = 3x5 + 2x -1 and the equation f x =0.

Answered: Consider the function f(x) = 3x° + 2x –…

Math

Advanced Math

Consider the function f(x) = 3x° + 2x – 1 and the equation f(x) = 0.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter8: Linear Functions

Section8.2: Linear Equations In Two Variables

Problem 2E

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Question

Consider the function f(x) = 3x³ + 2x – 1 and the equation f(x) = 0.

(d) Use Newton's method to approximate r to eight correct decimal places (starting
with xo = 0.5). Report the approximation xe, number of steps needed, and the
backward error |f(xc)|.
(e) Modify the code on Newton's method in order to solve the equation using Halley's
method, an iterative process given by
2f(xk) f'(xk)
Xk+1
H(xk) = Xk
2(f'(x))? – f(Xx)f"(xx) *
0.5). Report
Approximate r to eight correct decimal places (starting with xo =
the approximation xe, number of steps needed, and the backward error |f (xc)]-

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