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The following equation defines how the velocity of a slow-moving vehicle varies with time where the velocity V is in (m/s] and time t is in [s]. V = 0.5t + 2t/2 a) Use Romberg Integration to determine the displacement x of the vehicle in [m] from t = 0 to 10 [s). Continue iterating until the approximate percent relative error leal is less than 1%. b) Use the 3-point Gauss Quadrature method to determine the displacement x of the vehicle in (m) from t = 0 to 10 (s). Determine the true value of the displacement and the true percent relative error of the numerical result, lel.

The following equation defines how the velocity of a slow-moving vehicle varies with time where the velocity V is in (m/s] and time t is in [s]. V = 0.5t + 2t/2 a) Use Romberg Integration to determine the displacement x of the vehicle in [m] from t = 0 to 10 [s). Continue iterating until the approximate percent relative error leal is less than 1%. b) Use the 3-point Gauss Quadrature method to determine the displacement x of the vehicle in (m) from t = 0 to 10 (s). Determine the true value of the displacement and the true percent relative error of the numerical result, lel.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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The following equation defines how the velocity of a slow-moving vehicle varies with time where the velocity V is in [m/s] and time t is in [s]. V = 0.5t + 2t/2 a) Use Romberg Integration to determine the displacement x of the vehicle in [m] from t = 0 to 10 [s). Continue iterating until the approximate percent relative error leal is less than 1%. b) Use the 3-point Gauss Quadrature method to determine the displacement x of the vehicle in [m] from t = 0 to 10 (s]. Determine the true value of the displacement and the true percent relative error of the numerical result, lel. c) Use Richardson Extrapolation to determine the acceleration of the vehicle at t = 5 [s). Use step sizes of h, = 1 (s) and h, = 0.5 (s) and use the forward difference approximation of O(h) for the initial approximations. Determine the true value of the acceleration and the true percent relative error, leel, of the numerical approximation.
Transcribed Image Text:The following equation defines how the velocity of a slow-moving vehicle varies with time where the velocity V is in [m/s] and time t is in [s]. V = 0.5t + 2t/2 a) Use Romberg Integration to determine the displacement x of the vehicle in [m] from t = 0 to 10 [s). Continue iterating until the approximate percent relative error leal is less than 1%. b) Use the 3-point Gauss Quadrature method to determine the displacement x of the vehicle in [m] from t = 0 to 10 (s]. Determine the true value of the displacement and the true percent relative error of the numerical result, lel. c) Use Richardson Extrapolation to determine the acceleration of the vehicle at t = 5 [s). Use step sizes of h, = 1 (s) and h, = 0.5 (s) and use the forward difference approximation of O(h) for the initial approximations. Determine the true value of the acceleration and the true percent relative error, leel, of the numerical approximation.
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