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Unformatted text preview: Homework #4 1. (a) Starting with the initial guess of 1, find three additional approximations to the root of f ( x ) = x 2 2 using Newton’s method. (b) What is the absolute error of the final approximation? 2. (a) Consider f ( x ) = ( √ x, x ≥ √ x, x < . Starting with the initial guess of x = a > 0, find three additional approximations to the root of f ( x ) using Newton’s method. (b) Give a graphical description of how Newton’s method is arriving at the approxi mations. (c) Does Newton’s method converge to the exact root at 0 for x sufficiently close to 0? Why does this not violate the theorem on the convergence of Newton’s method? 3. (a) Starting with the initial guess of x = 1, find three additional approximations to the root of f ( x ) = ( x 2) 2 using Newton’s method. (b) What is the absolute error of the initial guess and each of the three approxima tions? Note the exact root is x * = 2....
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This note was uploaded on 10/17/2010 for the course MATH 174 taught by Professor Staff during the Spring '08 term at UCSD.
 Spring '08
 staff
 Addition, Approximation

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