Let positive real numbers a not equal to 2 and b not equal to 2.Consider the function: f(x) = a?x+ - 6abx? - 11b?Find intervals of positive initial guesses [c, d], where d > c> 0, for which Newton's Method:(i) converges to the positive root(ii) converges to the negative root(iii) is defined but does not converge to any root.Explain your answer.

Given function is fx =a2 x4 -6ab x2-11 b2 and a≠2, b≠12.

Answered: Let positive real numbers a not equal…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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USE NEWTON’S METHOD TO FIND P1
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03:A: Estimate the roots of the function f(x) = x² + x-3. by using Newton's method. B: Use the Newton-Raphson method of finding roots of | f(x) = 3x³ - 1.
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