The MATLAB question:

One numerical method for calculating the cubic root of a number VX is by using iterations. The process starts by choosing a value x1 as a first estimate of the solution. Using this value, a second a more accurate value X2 can be calculated with X2-6, + 2%)/3, which is then used for calculating a third, and accurate value x3, and so on. The general equation for calculating the value of xifrom x, is more Xi+1 Write an m-file which uses x 100 as the first estimate to calculate the cube-root of 100 (xthe cube root of the number you're calculating). Stop the looping when the relative error with each iteration is smaller than le-5. I.e. E =-tl- . Determine the number of iterations required to achieve this criterion and print out the value using fprintf. Xi E.g. The number of iterations required is 16 and the cube root of 999 is 9.996666, using x1-999