1. Determine the value of the smallest root in the interval [1,10] of o) =1-4 22 1+x (a) by using MATLAB to plot w = f(r) over the given interval. As part of your answer include a printout or write-up of the commands used to generate the graph, as well as a printout of the graph itself. (b) using 5 iterations of the Bisection method (by hand) on the interval [1,3]. As part of your answer, include the approximate percent relative error at each iteration. (e) How many iterations would be required for the maximum true error to be less than 10-47 {d) With the help of Matlab, use the Bisection method on the starting interval [1, until the maximum true error is less than 1072 As part of your answer, include a printout or write-up of the commands and/or m-files used in MATLAB (if they are different from the Labs), and of the output generated. Clearly indicate the approximate value of the root, the stopping criterion used, and the number of iterations needed. 2. Consider flxr) = e toosx. (a) Use 2 iterations of Newton's method (by hand) with zgp = 2 to estimate the value of a root of f{z). As part of your answer, include the value of |eg| at each iteration. (b) Use 1 iteration of the secant method (by hand) with xg = 1 and 21 = 2, to estimate the value of a root of f(z). As part of your answer, include the value of |ea| for your iteration. () With the help of Matlab, do & iterations of the secant method with g = 1 and =, = 2, to estimate the value of a root of f(z). Include the value of |eg| at the last iteration, and comment on the number of significant digits that are expected to be correct. As part of your answer, include a printout or write-up of the commands and/or m-files used in MATLAB (if they are different from the Labs), and of the output generated. Clearly indicate the approximate value of the root, the stopping criterion used, and the number of significant digits that are expected to be correct. 3. Using fractions throughout your calculations, solve rybrot+xyg = 0 2rirat+ra = 6 4r) + Bra + 229 = -14 (a) using naiive Gaussian elimination and backward substitution (by hand), (b) using Gaussian elimination with partial pivoting and backward substitution (by hand)