Please do the following questions with the code required and correct indentations 5.In this problem you will need to use complex number arithmetic. Assume that theequation 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 thatf'(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'smethod with complexstep.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 valueof the derivative df to be the new approximation Im(f(ro+ih))/h.Assume that|æk+1=x*|kx|kx* |rwhere 2* is such that f(r*) = 0. This means that the convergence rate of the new method isr. Estimate the convergence rate r using the equation r(e/2 + 1) = 0 and ro = 2.5. Studythe influence of the parameter h in the convergence rate.lim= C > 0,

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 f € C³ [a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) Im(f(ro+ih))/h + h²f" (ro)/6+0(h¹), = Where i is the imaginary unit such that i2 = -1.

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 f € C³ [a, b]. (a) Let h> 0 be a small number. Using appropriate Taylor expansion show that f'(ro) Im(f(ro+ih))/h + h²f" (ro)/6+0(h¹), = Where i is the imaginary unit such that i2 = -1.

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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