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Root Finding Methods: Newton, Bi-section, and Secant

Learn the mechanics of Newton's, Bi-section, and Secant root finding methods applied to f(X)=X^2-3 function with detailed steps and key variables. Enhance your understanding of numerical methods for root approximation.

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Root Finding Methods: Newton, Bi-section, and Secant

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  1. The mechanics of Newton, Bi-section, and Secant methods Use 3 its of Newton to fine the root of f(X)=X2-3 near X =1 X=Xold +( -F/Fdash) Use 3 its of Bi-section to fine the root of f(X)=X2-3 between X =1 and X=2 XM=(XL+XR)/2 Use 3 its of Secant to fine the root of f(X)=X2-3 between X =1 and X=2 XM=XR-FR*[(XL-XR)/FL-FR) Key: XL—guess left of root, XR—guess right of root, XM—new guess between XL and XR, Xold—old guess, X updated guess---FL = f(XL), FR=f(XR), FM=f(XM), F=f(Xold), Fdash=f’(Xold)

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