Problem 3: Numerical Algorithm for Determining Roots The only mathematical operations the processor in a computing device (calculator, computer, cell phone, etc.) can perform are addition, subtraction, multiplication, and division. With this rather limited set of operations, how does your calculator (or Excel and MATLAB) determine values for more complicated mathematical operations such as: x", x!, x, sin(x), cos(x), In(x), e*, atan (0) To calculate values for these functions, an iterative algorithm or a numerical method that only requires the basic arithmetic operations of addition, subtraction, multiplication, and division is needed. In this problem, you will look at a very simple algorithm for computing the cube root of a number based on the Newton-Raphson algorithm. The algorithm is very simple. We want to find = VN * See how close you are Error- abs (EstA3-N) Est3-N Make an initial guess for x: Est Within a for loop, update the estimate as follows: Est- Est- 3 Est2 Recalculate the Error using the new estimate Repeat this process to obtain a better guess usin the user . the number of iterations specified by . Write a MATLAB script that does the following: 1. Prompts the user for the Number, N, for which he or she wishes to find the cube root 2. Prompt the user for the number of iterations he or she wishes to perform 3. Set the initial guess to 1 4. Uses the algorithm describe above to repeatedly update the estimate and error for the