Given a function f(x) = 0.2e2x – 0.72x² – 0.19x + 3.11. Approximate the first derivative of the above function by using backward difference approximation, O(h²) at x = 1.13 by using 2 step sizes h = 0.125 and h = 0.25. ii. Given the true value of f'(1.13) is 2.0160. Calculate the percentage relative error of each step sizes in (i). ii. Based on your answer in (ii), there are a large number of percentage relative error for both step sizes. Give your suggestion on how to obtain a better approximation.
Given a function f(x) = 0.2e2x – 0.72x² – 0.19x + 3.11. Approximate the first derivative of the above function by using backward difference approximation, O(h²) at x = 1.13 by using 2 step sizes h = 0.125 and h = 0.25. ii. Given the true value of f'(1.13) is 2.0160. Calculate the percentage relative error of each step sizes in (i). ii. Based on your answer in (ii), there are a large number of percentage relative error for both step sizes. Give your suggestion on how to obtain a better approximation.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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