MATLAB

n 1. I would like to know the digits of V7. My calculator tells me they are 2.645751311064591. But how does my calculator know? One idea is to consider 7 as the root of the function f(x) = x2 7 and apply a root-finding method to estimate the digits. (a) (2 points) Use all three methods to estimate V7. Use an initial interval of [2,3] and a stopping tolerance of 10-5 (that's le-5 in Matlab), and initial guesses of x0 = 2 and x1 = 3. Report for each method (1) the approximate root with eleven digits shown after the decimal place, and (2) the number of iterations required. Fill in the answers organized like the table below. You will be reporting six quantities on this part (the middle two columns). Hint: at the end of your driver script, print the values of the variables you need, and nothing else. That way, when you hit Run you will just see the answers in the command window. Method Approx Error V7 2.64575131106 n/a n/a Bisect Newton Secant (b) (2 points) Report the magnitude of the exact error from each method. Note: please don't change your algorithm codes! Use the outputs in your driver script to compute the thee errors. Use scientific notation (that's format Shorts in Matlab) to display your answers with three or four significant digits. Add this information to the far-right column of the table above. (c) (4 points) Repeat this task one more time, except this time use a stopping tolerance of 10-10 (that's le-10 in Matlab). Use the same initial guesses as before. Report (1) the approximate root, (2) the number of iterations, and (3) the magnitude of the exact error, formatted the same in the tabular format as earlier. Hint: you only need to change one line of code in your driver script to accomplish this task. Method Approx Error 77 2.64575131106 n/a n/a Bisect Newton Secant n