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Please do the following questions with the full python coding and explanation below each question typed

Please do the following questions with the full python coding and explanation below each question typed

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

5. In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0 has a unique solution in an interval [a, b], and that fe C³ [a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) = Im(f(xo +ih))/h + h²f" (xo)/6+0(hª), (b) Where i is the imaginary unit such that i2= -1. Since f'(ro) Im(f(xo + ih))/h, consider the following modification of Newton's method with complex step. f(xk) Im(f(xk+ih)) Tk+1=kh- k = 0, 1, 2,... with given ro. Modify your code with Newton's method of problem 4 so as the default value of the derivative df to be the new approximation Im(f(ro+ih))/h. Assume that |æk+1=x*| kx|kx* |r where 2* is such that f(r*) = 0. This means that the convergence rate of the new method is r. Estimate the convergence rate r using the equation r(e/2 + 1) = 0 and ro = 2.5. Study the influence of the parameter h in the convergence rate. lim = C > 0,
Transcribed Image Text:5. In this problem you will need to use complex number arithmetic. Assume that the equation f(x) = 0 has a unique solution in an interval [a, b], and that fe C³ [a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) = Im(f(xo +ih))/h + h²f" (xo)/6+0(hª), (b) Where i is the imaginary unit such that i2= -1. Since f'(ro) Im(f(xo + ih))/h, consider the following modification of Newton's method with complex step. f(xk) Im(f(xk+ih)) Tk+1=kh- k = 0, 1, 2,... with given ro. Modify your code with Newton's method of problem 4 so as the default value of the derivative df to be the new approximation Im(f(ro+ih))/h. Assume that |æk+1=x*| kx|kx* |r where 2* is such that f(r*) = 0. This means that the convergence rate of the new method is r. Estimate the convergence rate r using the equation r(e/2 + 1) = 0 and ro = 2.5. Study the influence of the parameter h in the convergence rate. lim = C > 0,
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