Question: Utilizing Mathematica, please help me solve Problem 3 parts (a), particularly (b), (c) and (d). 3. Consider the function f(x) = xe-x 0.16064 (a) use

Utilizing Mathematica, please help me solve Problem 3 parts (a), particularly (b), (c) and (d).

3. Consider the function f(x) = xe-x 0.16064 (a) use FindRoot to locate a root between x = 2 and x = 3. (b) Write a program in Mathematica implementing the secant method (without bracketing). Use your program to locate a root near x = 3. Set the maximal number of iterations to 100 and the kick out threshold to 10-5. Display the approximate root, residual and |Xn Xn-1| at each iteration in a table. (c) How many iterations does your program actually execute before it stops? Comment on the speed of convergence of the Newton's method in problem 1 with the Secant method? (d) Use ListPlot to display 5 Newton's method estimates along with 5 secant method estimates. Use different symbols for the two plots. Comment on your results

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