The function f(x) = (x + 6)³ — 2ex² has two roots between x = −7 and x = 11. - 1. Plot f(x), -7 < x < 11 2. Use the Bisection method to estimate the lesser of the two roots and the Newton-Raphson method, the larger root, correct up to seventh decimal places. 3. For each method used in (2), calculate E¹, where is the relative error and i = 1, 2, ..., 25 (series of iterations). Superimpose on a graph their (i, E¹) points, using different marker type or line of color for each method and adding a legend to distinguished one method from the others. Label horizontal and vertical axes "No. of Iterations" and "Errors", respectively and put the title "Convergence Plots" above the graph.
The function f(x) = (x + 6)³ — 2ex² has two roots between x = −7 and x = 11. - 1. Plot f(x), -7 < x < 11 2. Use the Bisection method to estimate the lesser of the two roots and the Newton-Raphson method, the larger root, correct up to seventh decimal places. 3. For each method used in (2), calculate E¹, where is the relative error and i = 1, 2, ..., 25 (series of iterations). Superimpose on a graph their (i, E¹) points, using different marker type or line of color for each method and adding a legend to distinguished one method from the others. Label horizontal and vertical axes "No. of Iterations" and "Errors", respectively and put the title "Convergence Plots" above the graph.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Transcribed Image Text:The function f(x) = (x+6)³ - 2ex² has two roots between x = -7 and x = 11.
1. Plot f(x), -7 < x < 11
2. Use the Bisection method to estimate the lesser of the two roots and the Newton-Raphson
method, the larger root, correct up to seventh decimal places.
3.
For each method used in (2), calculate E¹, where is the relative error and i = 1, 2, ..., 25
(series of iterations). Superimpose on a graph their (i, E¹) points, using different marker type
or line of color for each method and adding a legend to distinguished one method from the
others. Label horizontal and vertical axes "No. of Iterations" and "Errors", respectively and put
the title "Convergence Plots" above the graph.
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