Let R denote any positive number. Newton's method is often used to determine an iterative formula for calculating frequently-used functions of R on computers and calculators; for example, to compute VR, VR, or V R for any given value of m, or 1/R (using only addition and multiplication), and so on. The basic idea is to find an equation f()-0 that has the value you want to compute (for example, VR) as one of its roots, and then apply Newton's method to compute a root of this equation. If you run Newton's method and it converges then it will converge to the desired answer. For example, a--vR are the only zeros of the function f(x) 2.2-R. If Newton's method is applied using this particular f(x), the following iterative formula is obtained f'(xi) If this sequence of values x converges to a value , then must be a zero of f(x); that is, x = VR. Thus, the iterative formula (*) can be used to compute square roots using only addition and division. (a) (2 points) Let m 2 2 denote any positive integer. Apply Newton's method to in order to determine an iterative formula (similar tofor computing VR. Simplify your iterative formula so that it is in a form that looks exactly like the rightmost part of (*) when m 2 (b) (2 points) Write a MATLAB function M-file to compute VR based on the iterative formula in (a). This M-file can be obtained by modifying the Newton function you wrote in question 1 as follows change the function header to function root- mth_root (m, R, x0, eps, imax) and replace the line root 10-f(xo) / f, (xo) by an expression for computing root by the formula in (a) above. Save this function as mth root.m. Note that mth root.m does not need to call any functions f or fp. Your iterative formula from (a) contains the particular functions f and fp that are required to compute VR. If you modify Newton as described here, then each successive computed approximation to VR will be output to your screen. Print a copy of your MATLAB function mth.root.m and hand it in. (c) (2 points) Use mth-root .m with m-3, R-2, to 1, eps-10-12 and imax-20 to compute an approximation to r. Print and hand in the MATLAB output