Exercise 4B (1) Write a function which takes a list of the coefficients of a polynomial P(x) = ª₁ + ª₁x + a² + ... + a₂x² of arbitrary degree n,

and a value of x, and returns P(xo). You can use the function given in lectures, ensuring you understand how it works. (2) Use the function to evaluate (a) P₁(x) = x³ + x² + 5x + 1 at x = 2. (b) P₂(x) = 5 x² at x = √3. 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 Maclaurin series for the natural logarithm ln(1 + x) is given by =(−1)n+1 xn n In(1+x) : = n=1 =x- x² x³ + 2 3 for all x. Use the first five terms in this series in the Horner evaluation function at a suitable value of x to give an approximation of In 3/2. (4) (a) Use your Horner's method function to evaluate the polynomial (x - 2)4 at the point x = 2.0001. (b) Is this answer correct? (c) Give brief reasoning for this answer. (5) In week 3 we wrote a function to convert from binary to decimal. The efficiency of this function can be improved using the same principle as Horner's method. Write such a function (horner_ternary_to_dec) using the ideas of Horner's method which takes a list containing Os, 1s and 2s (representing a base-3 number) and returns the corresponding decimal integer (so the input [1,2,0] returns the integer 15).