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b) Given the following data in table below: f(x) 9.367879 8.233241 7.180350 6.209329 -3.0 -2.8 -2.6 -2.4

b) Given the following data in table below: f(x) 9.367879 8.233241 7.180350 6.209329 -3.0 -2.8 -2.6 -2.4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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a) Construct the error formula for the first derivative f'(x) of three-point formula when considering polynomial at three points, xp, X1 and x2, then let x=x,. Show your steps clearly. b) Given the following data in table below: f(x) -3.0 9.367879 8.233241 7.180350 6.209329 -2.8 -2.6 -2.4 Approximate f'(-2.6) using two-point formula and three-point formula (choose either forward, backward or centre). Which formula should give the best result? Provide explanation to support your answer.
Transcribed Image Text:a) Construct the error formula for the first derivative f'(x) of three-point formula when considering polynomial at three points, xp, X1 and x2, then let x=x,. Show your steps clearly. b) Given the following data in table below: f(x) -3.0 9.367879 8.233241 7.180350 6.209329 -2.8 -2.6 -2.4 Approximate f'(-2.6) using two-point formula and three-point formula (choose either forward, backward or centre). Which formula should give the best result? Provide explanation to support your answer.
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