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Jse the Bisēčtión Method to find the first root of f(x) = -12 – 21x + 18x² -12 - 21a + 18x2 - 2.75³. In %3D doing so, use the initial guesses (bracket) of a = -1 and b= 0 with a stopping criterion of 1% relative error (also known as relative or approximation error), as given by %3D rold x 100%

Jse the Bisēčtión Method to find the first root of f(x) = -12 – 21x + 18x² -12 - 21a + 18x2 - 2.75³. In %3D doing so, use the initial guesses (bracket) of a = -1 and b= 0 with a stopping criterion of 1% relative error (also known as relative or approximation error), as given by %3D rold x 100%

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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xnew Use the Bisection Method to find the first root of f(x) = -12 - 21c + 182 – 2.75.x°. In doing so, use the initial guesses (bracket) of a = -1 and b = 0 with a stopping criterion of 1% relative error (also known as relative or approximation error), as given by xnew pold m, Crel = x 100% < e = 1% where re is the midpoint for the current interval (really, the current estimate of the root) and xold is that for the latest previous iteration. After you have implemented the Bisection Method to find the first root, plot the function f (x) from r = -2 to r = 7 (i.e. these are the x-limits). Using the hold on command, plot your estimate of the root on top of the original plot using a single marker that is of a different style and color than the main plot (for example, plot the range of values in blue with x-markers, and overlay the first root with a red circle marker). This plotting serves as a "sanity check" for the reasonableness of your results. Hints: • You can treat f as an anonymous function so that you can easily pass values of x to f as an argument without having to re-define the expression for f. Example syntax: my_fun = @(x) 2 + 5*x • If you are going to pass a vector of input values to your function f (for example, when plotting) then make sure to use the "dot" operator for element-wise operations (e.g., ". instead of "** etc. to avoid non-conformable errors). • Explore the documentation for the built-in function plot or the plotting examples from class to beautify your figure.
Transcribed Image Text:xnew Use the Bisection Method to find the first root of f(x) = -12 - 21c + 182 – 2.75.x°. In doing so, use the initial guesses (bracket) of a = -1 and b = 0 with a stopping criterion of 1% relative error (also known as relative or approximation error), as given by xnew pold m, Crel = x 100% < e = 1% where re is the midpoint for the current interval (really, the current estimate of the root) and xold is that for the latest previous iteration. After you have implemented the Bisection Method to find the first root, plot the function f (x) from r = -2 to r = 7 (i.e. these are the x-limits). Using the hold on command, plot your estimate of the root on top of the original plot using a single marker that is of a different style and color than the main plot (for example, plot the range of values in blue with x-markers, and overlay the first root with a red circle marker). This plotting serves as a "sanity check" for the reasonableness of your results. Hints: • You can treat f as an anonymous function so that you can easily pass values of x to f as an argument without having to re-define the expression for f. Example syntax: my_fun = @(x) 2 + 5*x • If you are going to pass a vector of input values to your function f (for example, when plotting) then make sure to use the "dot" operator for element-wise operations (e.g., ". instead of "** etc. to avoid non-conformable errors). • Explore the documentation for the built-in function plot or the plotting examples from class to beautify your figure.
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