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Newton-Raphson Method Description of task. 21. This is a method which involves using an iterative formula, f(x) t f'(x₁) 22. State the equation you are trying to solve, which is f(x) = 0, where you define what your f(x) is. (There should be a different f(x) used for each method.) 23. You must find all the roots using this method. 24. Show how you differentiated your f(x) to get f '(x) to put into the Newton- Raphson iterative formula but with your f (x) and f'(x) substituted in the appropriate places. 25. Show a graph of your y = f(x), pointing out the roots that you are trying to find. 26. Show your calculations, and clearly state the integer near the root that you have chosen to be your x values. Is this required? Yes or No Completed? Date?

Newton-Raphson Method Description of task. 21. This is a method which involves using an iterative formula, f(x) t f'(x₁) 22. State the equation you are trying to solve, which is f(x) = 0, where you define what your f(x) is. (There should be a different f(x) used for each method.) 23. You must find all the roots using this method. 24. Show how you differentiated your f(x) to get f '(x) to put into the Newton- Raphson iterative formula but with your f (x) and f'(x) substituted in the appropriate places. 25. Show a graph of your y = f(x), pointing out the roots that you are trying to find. 26. Show your calculations, and clearly state the integer near the root that you have chosen to be your x values. Is this required? Yes or No Completed? Date?

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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USE NEWTON RAPHSON METHOD , PLEASE FOLLOW THE TASK DESCRIPTION
APM Project- The task, instructions and marking guidelines. Newton-Raphson Method Description of task. Is this required? Yes or No 21. This is a method which involves using an iterative formula, f(x₁) Xn+= Xn= f'(x₁) 22. State the equation you are trying to solve, which is f(x) = 0, where you define what your f(x) is. (There should be a different f(x) used for each method.) 23. You must find all the roots using this method. 24. Show how you differentiated your f(x) to get f '(x) to put into the Newton- Raphson iterative formula but with your f (x) and f' (x) substituted in the appropriate places. 25. Show a graph of your y = f(x), pointing out the roots that you are trying to find. 26. Show your calculations, and clearly state the integer near the root that you have chosen to be your x values. 27. Show a zoomed-in graph showing the tangents used in this method (it looks like a zig-zag, or saw-tooth), with the first three x values labelled (x. to x₂). 28. Describe how the iterations are performed and the x, values converge to the root, referring to both your calculations table and your zoomed-in graph illustration. 29. Perform a change of sign check by looking at f(x) for x values 0.000005 above and below your root. Explain why you had to do this. 30. State that your root is x = ...... with a maximum error of ±0.000005 31. Repeat steps 4, 7 and 8 for all the other roots. (You do not need to illustrate these, but you must show full calculations.) 32. Repeat steps 1. to 4. then explain why the Newton Raphson was not able to produce a value for x1. 33. Show a graph of your f(x) with a tangent drawn at (x. (this should be parallel to the x-axis) and use this to illustrate graphically why the method has failed to locate the root in this case. Completed? Date?
Transcribed Image Text:APM Project- The task, instructions and marking guidelines. Newton-Raphson Method Description of task. Is this required? Yes or No 21. This is a method which involves using an iterative formula, f(x₁) Xn+= Xn= f'(x₁) 22. State the equation you are trying to solve, which is f(x) = 0, where you define what your f(x) is. (There should be a different f(x) used for each method.) 23. You must find all the roots using this method. 24. Show how you differentiated your f(x) to get f '(x) to put into the Newton- Raphson iterative formula but with your f (x) and f' (x) substituted in the appropriate places. 25. Show a graph of your y = f(x), pointing out the roots that you are trying to find. 26. Show your calculations, and clearly state the integer near the root that you have chosen to be your x values. 27. Show a zoomed-in graph showing the tangents used in this method (it looks like a zig-zag, or saw-tooth), with the first three x values labelled (x. to x₂). 28. Describe how the iterations are performed and the x, values converge to the root, referring to both your calculations table and your zoomed-in graph illustration. 29. Perform a change of sign check by looking at f(x) for x values 0.000005 above and below your root. Explain why you had to do this. 30. State that your root is x = ...... with a maximum error of ±0.000005 31. Repeat steps 4, 7 and 8 for all the other roots. (You do not need to illustrate these, but you must show full calculations.) 32. Repeat steps 1. to 4. then explain why the Newton Raphson was not able to produce a value for x1. 33. Show a graph of your f(x) with a tangent drawn at (x. (this should be parallel to the x-axis) and use this to illustrate graphically why the method has failed to locate the root in this case. Completed? Date?
Newton Raphson method f(x) = 5x² - 4x² −6,
Transcribed Image Text:Newton Raphson method f(x) = 5x² - 4x² −6,
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