CHME 312, Spring 2017 Homework 5 Due Friday 03/13/17 Note: Please follow the submission guidelines properly. One SINGLE file submission. Name your file in this format: _.. For example: smith_hw1.pdf. COPY your Matlab code into your document. DO NOT take a screenshot of your code and paste it in your document as image. Remember to include the outputs/plots/tables in your submission. A wrong format or partial submission will affect your score. Problem 1: (a) Fit the following dataset using Chebyshev polynomial as basis functions of the form between [-1,1]. T0 (x) = 1 T1 (x) = x x f(x) -1 98.001 -0.5556 30.384 -0.1110 1.221 0.3333 11.038 0.7778 60.360 Decide and explain your choice of \"n\" based on the number of data points. Do not use Matlab builtin functions (such as polyfit). You can perform the detailed steps by writing Matlab code accordingly. (b) Now use Matlab function polyfit and compare your results in (a) with it. Problem 2: Use Newton's Forward and Backward approximation method to find the function value at x = 1.72 by hand. x f(x) 1.7 0.3979849 1.8 0.3399864 1.9 0.2818186 2.0 0.2238908 If f(x=1.72) = 0.3864185, calculate your errors in both cases. Problem 3: The distance x of a runner from a fixed point is measured (in metres) at intervals of half a second. The data obtained is (a) Use forward differences to approximate the runner's velocity at t = 0.5s. (b) Use backward difference to approximate the runner's velocity at t = 1.25s. (c) Use a central difference to approximate the runner's acceleration at t = 1.5s. Problem 4: Using Simpson's 3/8 rule (n=10) and trapezoidal rule (n=10), integrate the following and comment on the accuracy of the results compared to the analytical value. ! =