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Use Romberg integration to approximate the integrals in Exercise 2 to within 10~6

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 6 Chapter 4.5

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 6

Use Romberg integration to approximate the integrals in Exercise 2 to within 10~6 . Compute the Romberg table until either |Rn_i._i R,| < 10-6 or n = 10. Compare your results to the exact values ofthe integrals.

Step-by-Step Solution:
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MAT 211­ Lecture 6­ 15.3 & 15.4 Section 15.3 Homework #8: ln(x,y)= x​ +y​2­y​x­2 lnx= 0 & lny= 0 1st Derivative:​ lnx= 2x­y​ lny= 2y­2yx I. 2x­y​=0 ­­­­­­­> x=1 2­y​=0 2=y​ y=­ 2 2​ 2y­2yx=0 ­­­­­­­> y=0 2x­y​ =0 2x­0=0 x=0 II. 2y(1­x)= 0 y=0 & x=1 Critical Points: (0,0); (1, ­ 2); (1, + 2) 2nd Derivative:​ lnxx= 2 lnxx (0,0)= 2 lnyy= 2­2x lnyy (0,0)= 2 lnxy= ­2y lnxy (0,0)= 0 H(0,0)= 2 * 2 ­ 0= 4 Since lnxx= 2>0, then we have a relative minimum at (0,0). ­Critical point at (1, ­ 2) : lnxx (1, ­ 2) =2 √

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Chapter 4.5, Problem 6 is Solved
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Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

The answer to “Use Romberg integration to approximate the integrals in Exercise 2 to within 10~6 . Compute the Romberg table until either |Rn_i._i R,| < 10-6 or n = 10. Compare your results to the exact values ofthe integrals.” is broken down into a number of easy to follow steps, and 37 words. The full step-by-step solution to problem: 6 from chapter: 4.5 was answered by , our top Math solution expert on 03/16/18, 03:24PM. Since the solution to 6 from 4.5 chapter was answered, more than 237 students have viewed the full step-by-step answer. Numerical Analysis was written by and is associated to the ISBN: 9781305253667. This textbook survival guide was created for the textbook: Numerical Analysis, edition: 10. This full solution covers the following key subjects: . This expansive textbook survival guide covers 76 chapters, and 1204 solutions.

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Use Romberg integration to approximate the integrals in Exercise 2 to within 10~6