Exercise 4B(1) Write a function which takes a list of the coefficients of a polynomialP(x) = ª₁ + ª₁x + a² + …..+anxnof arbitrary degree n, and a value of x, and returns P(x). You can use the function given in lectures,ensuring you understand how it works.(2) Use the function to evaluate(a) P₁(x) = 4x4 + 3x² + 2 at x = 2.(b) P₂(x) = 2 — ¹x¹ at x = √√/2.Are these answers exact? Explain why or why not.(Use a print statements to show the evaluation of your function, and answer the question in a comment.)(3) The power series for the sine function sin(x) is given by∞x2n+1(2n + 1)!sin(x) = Σ(−1)”.n=0= x6+x5120for all x. Use the first four terms in this series in the Horner evaluation function at a suitable value of a togive an approximation of sin(π/4).(4) (a) Use your Horner's method function to evaluate the polynomial (x − 1)³ at the pointx = 1.000001.(b) Is this answer correct?(c) Briefly explain why, or why not.(5) In week 3 we wrote a function to convert from binary to decimal. This can be adapted to otherbases, here will explore octal (base 8). The efficiency of the function we wrote can be improved using thesame principle as Horner's method. Write such a function (horner_octal_to_dec) using the ideas ofHorner's method which takes a list whose entries are integers between 0 and 7, where the list representsa base-8 number, and returns the corresponding decimal integer (so the input [2,5,1] returns theinteger 169).

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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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Exercise 4B (1) Write a function which takes a list of the coefficients of a polynomial P(x) = ª₁ + ª₁x + a² + ... + anxn of arbitrary degree n, and a value of xo, and returns P(xo). You can use the function given in lectures, ensuring you understand how it works.