a) f(x)= arctan(2(x - 1)) - In [x]. Plot (using PYTHON) the graph of the function f(x) and describe the intervals of monotonicity of the function f. Speak also about the roots of the equation f(x) = 0. 5) Prove by analytical means (using Calculus), that the equation f(x) = 0 has exactly four real roots P1 P2 P3 P4. e) Find approximations of the roots using the codes of Problems 1 and 2, with input parameters o, TOL and NMAX of your choice (try xo values close to the real roots). d) Compare the results and the CPU times elapsed with the results ob- tained by using the PYTHON functions scipy. optimize.bisect, scipy.optimize.newton andscipy. optimize.fsolve. What do you observe? Finally, take TOL-1.e-6, NMAX=50 and execute your implementation of Newton's method with xo = -1, 0.65, 0.7, 1.7, 1.8, 1.9, 5 and 10. Comment on the results.

a) f(x)= arctan(2(x - 1)) - In [x]. Plot (using PYTHON) the graph of the function f(x) and describe the intervals of monotonicity of the function f. Speak also about the roots of the equation f(x) = 0. 5) Prove by analytical means (using Calculus), that the equation f(x) = 0 has exactly four real roots P1 P2 P3 P4. e) Find approximations of the roots using the codes of Problems 1 and 2, with input parameters o, TOL and NMAX of your choice (try xo values close to the real roots). d) Compare the results and the CPU times elapsed with the results ob- tained by using the PYTHON functions scipy. optimize.bisect, scipy.optimize.newton andscipy. optimize.fsolve. What do you observe? Finally, take TOL-1.e-6, NMAX=50 and execute your implementation of Newton's method with xo = -1, 0.65, 0.7, 1.7, 1.8, 1.9, 5 and 10. Comment on the results.

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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