Unformatted text preview: Iteration Fonnula) Let f be a function and let Xo bean initial guess for a root. For /l ~ 0, Horizontal Tangent Lines: Although it is unlikely, it is possible that at some guess X n , f'(x n ) == O. Of course, at this point Newton's Iteration Formula becomes undefined and the process fails. In graphical terms, the tangent line at x n is horizontal, and so it never intersects the x~axisto produce the next guess! NearHorizontal Tangent Lines: If the tangent line at x n is nearhorizontal, the xintercept of the tangent line could take us far away from the desired root. At the very least, it will take several iterations to get back to the desired root. What's worse, fmay have a second root out near this faraway xintercept. If this is the case, Newton's method will work beautifully, but will find tlus second root instead of the desired root!...
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 Spring '11
 Teague
 Calculus, Equations

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