In both questions, take a as the last 2 digits of your student Id number.

Q1 Consider the nonlinear equation

(a) Write the general term x_n of the Newtons iteration sequence with an arbitrary initial value x₀ for the given equation. (b) Write a Python program which computes the iterations of the Newtons method starting with x₀ = 3.a until |x_n+1 - x_n| 4 and prints the computed terms of the sequence {x_n} and the value of n for which |x_n+1 x_n| 4 holds. (c) Return your solution file containing the solution of part (a), the Python code and the output of your Python code. Q2 Consider the definite integral

(a) Write the Composite Simpsons rule formula with 2M subintervals.

(b) Write a Python program which computes the approximate value with the Composite Simpsons rule formula written in part (a), for M = 1, 2, 3, 4, 5, 6, 7, 8 and print the results as M = k, Sk =computed value, for k = 1, . . . , 8.

(c) Return your solution file containing the solution of part (a), the Python code and the output of your Python code.