Using Jupyter Notebooks in Python

Problem 1: Root finding 5 points] a. Write down the formula used get the approximation ri given ri-1 to the roots of f(x) and g(x) (given below) using Newton's root finding algorithm and implement the algorithm yourself -2013-50% f(x) g(x) 3x + 20 exp(0.5x) _ exp(0.62 + 4 = For both functions, start Newton's algorithm at x 0 and terminate after it converges to a stationary point such that the candidate root points r found at two successive steps do not differ up to the fourth significant fractional digit, i.e. |xi - xi-i| 0.0001. The output requirement is described in part b b. For each iteration of the algorithm, output the iteration number, the current estimate of the exp(-), you root and the value of the function there. For example, for f(x)log(z)-1 would show Iteration xi f(ai) 1.00000-0.63212 2.00000 -0.17152 2.47034-0.01109 2.50496-0.00005 2.50511-0.00000 c. Write a function to find the root of the function f(x) in part a. using the bisection method Run the function starting at a = 0 and b 1 . Output the value of a, b and f(x) evaluated at the midpoint of a and b at each iteration. Stop when lab0.0001. Comment of the speed of convergence compared to Newton's method for the same