Griffith School of Engineering Semester 2-2013 Gold Coast Campus 2006ENG Numerical and Data Analysis Laboratory Workshop Week 7 Include all your programs and their input and output in ONE .doc or .pdf file. Also, include all your comments on the same file. Submit the file using turn-it-in to be found in the assessment menu on your L@G account. Please be reminded that turn-it-in allows submission only once. The marks for the three questions are 6 + 5 + 9. 1. The “divide and average” method is an old-time method for approximating the square root of any positive number a > 0. The formulation is x = (x + a/x)/2. Write a MATLAB program to implement this algorithm. Your program will take an input a > 0 and an initial value of x > 0. It will then create a table showing the old and new values of x in each iteration. In each iteration, the table will also show the absolute relative errors |€t| and absolute relative apprximate errors |€a|. Stop until 10 iterations or |€a| falls below 0.1%. Include your program, its input and output in the file to be submitted. 2. Evaluate by hand the polynomial y = x3 – 7×2 + 8x – 0.356 at x = 1.373. Everytime you do a computation use chopping at 3 decimal places. Treat x3 as (x*x)*x and x2 as x*x. Use a calculator or MATLAB command window to compute. Express y as y = ((x – 7)x + 8)x – 0.356 and recompute this again by hand. Compute the true errors and also the difference between the two computed values. What types of error did happen in these cases? Comment on the efficiency of these methods in terms of the number of operations to be performed. Include all your workings in the file to be submitted. 3. The circle shown below has its center at (0.5, 0.5) and radius 0.5. The circle is inscribed within the rectangle. The rectangle has its corners at (0,0), (1,0), (1,1) and (0,1). The area of the circle is C = pr2 = 0.25p and that of the rectangle is R = d2 = 1. From these, we can derive C/R = 0.25p meaning p = 4*C/R. This means the value of p…