Matlab

One numerical method for calculating the cubic root of a number, 3 Squareroot Halley's method. The solution process starts by choosing a value x_1 as a first estimate of the solution. Using this value, a second, more accurate value x_2 is calculated with, x_2 = x_1(x_1^3 + 2P)/(2x_1^3 + P) which is then used for calculating a third, still more accurate value x_3 and so on. The general equation for calculating the value of x_i + 1 from the value of x_i is x_i + 1 = x_i(x_i^3 + 2P)/(2x_i^3 + P). Write a MATLAB program that calculates the cubic root of a number. In the program use x_1 = P for the first estimate of the solution. Then, by using the general equation in a loop, calculate new, more accurate values. Stop the looping when the estimated relative error E defined by E = |x_i + 1 - x_i/x_i) is smaller than 0.00001. Use the program to calculate: (a) 3 Squareroot 800 (b) 3 Squareroot 59071 (c) 3 Squareroot -31.55