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Determine the roots of f (x) = -12 – 21x + 18x – 2.75x using the false-position method, with initial guesses of xI=-1 and xu = 0 and a stopping criterion of 1%.

Determine the roots of f (x) = -12 – 21x + 18x – 2.75x using the false-position method, with initial guesses of xI=-1 and xu = 0 and a stopping criterion of 1%.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem #3** Determine the roots of \( f(x) = -12 - 21x + 18x^2 - 2.75x^3 \) using the false-position method, with initial guesses of \( x_l = -1 \) and \( x_u = 0 \) and a stopping criterion of 1%. **Equation:** \[ x_r = x_u - \frac{f(x_u)(x_l - x_u)}{f(x_l) - f(x_u)} \] **Graph Explanation:** The graph displays the function \( f(x) \) along with a shaded area representing the process of finding the root using the false-position method. The line intersects the x-axis, indicating an estimation of the root. The points \( x_l \) and \( x_u \) are marked on the x-axis as initial guesses, showing how they are used to draw the line that helps calculate \( x_r \), the estimated root. The shaded area underlines the iterative process of zeroing in on the root by updating \( x_l \) or \( x_u \) based on the function's value at \( x_r \).
Transcribed Image Text:**Problem #3** Determine the roots of \( f(x) = -12 - 21x + 18x^2 - 2.75x^3 \) using the false-position method, with initial guesses of \( x_l = -1 \) and \( x_u = 0 \) and a stopping criterion of 1%. **Equation:** \[ x_r = x_u - \frac{f(x_u)(x_l - x_u)}{f(x_l) - f(x_u)} \] **Graph Explanation:** The graph displays the function \( f(x) \) along with a shaded area representing the process of finding the root using the false-position method. The line intersects the x-axis, indicating an estimation of the root. The points \( x_l \) and \( x_u \) are marked on the x-axis as initial guesses, showing how they are used to draw the line that helps calculate \( x_r \), the estimated root. The shaded area underlines the iterative process of zeroing in on the root by updating \( x_l \) or \( x_u \) based on the function's value at \( x_r \).
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