Utilizing Mathematica, please help me solve Problem 1 parts (a) and (b).

1. Plot the function f(x) = 23 cos(x). (a) Use Find Root to locate a root near x = 3 (b) Write a program in Mathematica implementing Newton's method with a while loop instead of a For loop. Use your program to approximate the root near x = -1. Set the maximal number of iterations to 100 and the kick out threshold or tolerance, to 10-4. Display in a table the iteration number, the approximate root, the residual, \f (xn) and successive iteration errors, Xn Xn-1) at each iteration. How many iterations does your program actually execute before it stops? Using the result of (a) as the actual and this result as the computed, calculate the relative absolute error (same as relative error as defined in class) 1. Plot the function f(x) = 23 cos(x). (a) Use Find Root to locate a root near x = 3 (b) Write a program in Mathematica implementing Newton's method with a while loop instead of a For loop. Use your program to approximate the root near x = -1. Set the maximal number of iterations to 100 and the kick out threshold or tolerance, to 10-4. Display in a table the iteration number, the approximate root, the residual, \f (xn) and successive iteration errors, Xn Xn-1) at each iteration. How many iterations does your program actually execute before it stops? Using the result of (a) as the actual and this result as the computed, calculate the relative absolute error (same as relative error as defined in class)