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Write a Newton method root-finding function. Remember that for the Newton methcnly need to give a single initial estimate, but you also need to supply the derivative. You can give both input function and its derivative as lambdas. 1. Use Newton's method to verify that the function h(x) = 4 tan-¹ x has a root at x = 0. 2. Try to find this root with a starting guess of xo = 1, and then with an starting guess of xo = 1.5. What goes wrong in the second case? 3. Now consider the function h(x) = x² - 2 (which clearly has a root at x = √2) with an initial guess of xo = 0. What is the problem?

Write a Newton method root-finding function. Remember that for the Newton methcnly need to give a single initial estimate, but you also need to supply the derivative. You can give both input function and its derivative as lambdas. 1. Use Newton's method to verify that the function h(x) = 4 tan-¹ x has a root at x = 0. 2. Try to find this root with a starting guess of xo = 1, and then with an starting guess of xo = 1.5. What goes wrong in the second case? 3. Now consider the function h(x) = x² - 2 (which clearly has a root at x = √2) with an initial guess of xo = 0. What is the problem?

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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Write a Newton method root-finding function. Remember that for the Newton methc' +nly need to give a single initial estimate, but you also need to supply the derivative. You can give both input function and its derivative as lambdas. 1. Use Newton's method to verify that the function h(x) = 4tan¯¹ x has a root at x = 0. 2. Try to find this root with a starting guess of xo = 1, and then with an starting guess of Xx0 = 1.5. What goes wrong in the second case? 3. Now consider the function h(x) = x² – 2 (which clearly has a root at x = √2) with an initial 0. What is the problem? guess of co =
Transcribed Image Text:Write a Newton method root-finding function. Remember that for the Newton methc' +nly need to give a single initial estimate, but you also need to supply the derivative. You can give both input function and its derivative as lambdas. 1. Use Newton's method to verify that the function h(x) = 4tan¯¹ x has a root at x = 0. 2. Try to find this root with a starting guess of xo = 1, and then with an starting guess of Xx0 = 1.5. What goes wrong in the second case? 3. Now consider the function h(x) = x² – 2 (which clearly has a root at x = √2) with an initial 0. What is the problem? guess of co =
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