=N toApply Newton's method to the equation x²derive this algorithm for getting the square root of N:N5₁₁ - = (x + ²)=Xn+1

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Answered: Apply Newton's method to the equation…

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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B6. (a) Sketch the graphs of the left and right hand sides of the equation x* = 3 – x. Hence show graphically that the equation must have a root between x = 1 and x = 2. Show that the application of the Newton-Raphson method to this equation, after simplification, leads to the recursion formula 3 (x + 1) 4 x + 1 Xn+1 = (b) Taking a suitable initial guess at the root, xo, use the Newton-Raphson method to find an approximation to the root of x = 3 – x between x = 1 and x = 2 correct to 7 significant figures.
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Apply Newton's method to the equation x² = N to derive this algorithm for getting the square root of N: Xn+l 1 (² 2 n + N Xn