An algorithm for calculating the cubic root of a number, VP, starts by choosing a value x, as a first estimate of the root. Using this value, a second, more accurate value x, is calculated as X, = x(x + 2P)/(2x} +P), which is then used for calculating a third, still more accurate value Xy, and so on. The general equation for calculating the i+ 1 value from the ith value of x is X[+1 = x (x +2P)/(2x +P) A. (15 pts) Write a UDF HWYP2.m that calculates the cubic root of a number. The input argument to your function must be the number P and the output argument must be its cubic root x. The function must use x, = P for the first estimate of the root. Then by using the general equation in a while loop, the function calculates a new, more accurate value and repeats. The function must calculate the estimated relative error E = 1 between every 2 consecutive x values. You can use variable names xi and xipi for x, and X:-1, respectively. The loop must terminate once E <10-1° or the number of passes exceeds 50. At the end of the pass your must assign the value of xipl to xi to start a new iteration (trial). Use your function to calculate: a) V800 b) V59071 c ) V-31.55 d) V-10-5 Verify the output of your functions by the nthroot(P,3) B. (10 pts) Modify your function to work not only for scalars but also for any 2D array. You will need first to determine the dimensions mxn of the input array and then to preallocate an array of the outputs (Root3) to zeros (m, n). Then, you must nest your while loop from the previous part inside 2 other nested for loops, one for each array dimension. For every value of the input matrix P(ij), the function must determine its cubic root x as before and then save it in Root 3(1.j) such that the output of HW7P2 in will be similar to the output of nthroot(P, 3) when P is an array not a scalar. Use your function on the following arrays, 1) B 1 0.008 2764 0.125 2) E-11 B 0.027 -64 0.125; B 0,064 0.216 512 -0.001] 3) F = 11:5:10:-1:6: 11:15 Verify the output of your functions by the nthroot (P.3)