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2. In this problem consider Newton's method. (a) Write a PYTHON function computing an approximation of the root p of the equation f(x) = 0 using Newton's method. Specifically the code will compute the terms xn of the sequence f(xn) f'(xn)' Xn+1 = Xn- n = 0, 1, 2, ..., where to is a given initial guess (or approximation) of the root p. For stopping criterion use the following: If xn+1 n ≤ TOL for the first time, then return an+1 as approximation of the root p. Allow the code to do only NMAX iterations. At every step n, the code should print the values n, xn, f(n) and n+1-n. In case where the number of iterations reaches the maximum allowed number of iterations without satisfying the stopping criterion, then the code should print an error message, for example: "Failure: Algorithm fail to converge using only NMAX iterations". (b) Test your code by finding an approximate solution to the equation log(x) + x = 0 with an initial guess of your choice.

2. In this problem consider Newton's method. (a) Write a PYTHON function computing an approximation of the root p of the equation f(x) = 0 using Newton's method. Specifically the code will compute the terms xn of the sequence f(xn) f'(xn)' Xn+1 = Xn- n = 0, 1, 2, ..., where to is a given initial guess (or approximation) of the root p. For stopping criterion use the following: If xn+1 n ≤ TOL for the first time, then return an+1 as approximation of the root p. Allow the code to do only NMAX iterations. At every step n, the code should print the values n, xn, f(n) and n+1-n. In case where the number of iterations reaches the maximum allowed number of iterations without satisfying the stopping criterion, then the code should print an error message, for example: "Failure: Algorithm fail to converge using only NMAX iterations". (b) Test your code by finding an approximate solution to the equation log(x) + x = 0 with an initial guess of your choice.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Please do the following questions with the full python coding and explanation below each question typed

2. In this problem consider Newton's method. (a) Write a PYTHON function computing an approximation of the root p of the equation f(x) = 0 using Newton's method. Specifically the code will compute the terms xn of the sequence f(xn) f'(xn)' Xn+1 = Xn n = 0, 1, 2, ..., where xo is a given initial guess (or approximation) of the root p. For stopping criterion use the following: If |xn+1 − xn| ≤ TOL for the first time, then return xn+1 as approximation of the root p. Allow the code to do only NMAX iterations. At every step n, the code should print the values n, xn, f(xn) and n+1-n. In case where the number of iterations reaches the maximum allowed number of iterations without satisfying the stopping criterion, then the code should print an error message, for example: "Failure: Algorithm fail to converge using only NMAX iterations". (b) Test your code by finding an approximate solution to the equation log(x) + x = 0 with an initial guess of your choice.
Transcribed Image Text:2. In this problem consider Newton's method. (a) Write a PYTHON function computing an approximation of the root p of the equation f(x) = 0 using Newton's method. Specifically the code will compute the terms xn of the sequence f(xn) f'(xn)' Xn+1 = Xn n = 0, 1, 2, ..., where xo is a given initial guess (or approximation) of the root p. For stopping criterion use the following: If |xn+1 − xn| ≤ TOL for the first time, then return xn+1 as approximation of the root p. Allow the code to do only NMAX iterations. At every step n, the code should print the values n, xn, f(xn) and n+1-n. In case where the number of iterations reaches the maximum allowed number of iterations without satisfying the stopping criterion, then the code should print an error message, for example: "Failure: Algorithm fail to converge using only NMAX iterations". (b) Test your code by finding an approximate solution to the equation log(x) + x = 0 with an initial guess of your choice.
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