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3.8 Newton&acirc;€™s Method

# 3.8 Newton&acirc;€™s Method - From the initial...

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* Section 3.8 * Newton’s Method

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Newton’s Method is a technique  for approximating the real zeros of  a function.  It uses tangent lines to  approximate the graph of the  function near its x-intercepts.
Consider a function  f  that is  continuous on [a,b] and differentiable  on (a,b).  If  f(a)  and  f(b)  differ in sign, by  the Intermediate Value Thm.,  must  have at least one zero in (a,b).   Estimate where you think the zero  should occur:  x = x 1 x x 1 2 (x ,  f(x  ) 1 1

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Unformatted text preview: From the initial estimate x1, you obtain a new estimate: x2 = x1 – f(x1) f ’(x1) Repeated application of this process is called Newton’s Method. Each successive application of this procedure is called an iteration . * Newton’s Method for Approximating the Zeros of a Function * Joke Time * What did the judge say when the skunk walked in the courtroom? * Odor in the court! * What sound do porcupines make when they kiss? * Ouch!...
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