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Unformatted text preview: ··· = π 4 (2) [25 points] (a) Assuming the value of the Gaussian integral i ∞∞ ex 2 2 dx = √ 2 π Fnd i ∞ √ x ex dx (b) Prove that i ∞ x n + 1 2 ex dx = (2 n + 1)! n ! 2 2 n +1 √ π for n = 0 , 1 , 2 , . . . . 1 2 HOMEWORK SET 8 DUE AT 1:00 PM ON MONDAY, NOVEMBER 21, 2005 (3) [25 points] Use Newton’s method to try to solve x = ex starting with the guess x 1 = 0. What is the algorithm for x n +1 in terms of x n ? Use some program to implement the algorithm and Fnd the solution to 10place accuracy....
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This note was uploaded on 03/30/2010 for the course MA 1a taught by Professor Borodin,a during the Fall '08 term at Caltech.
 Fall '08
 Borodin,A
 Math

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