In this assignment sometimes you will be given a question with values depending on your ID number. Assume klm is the last 3 digits. For example, if your ID number is 200205678, k = 6,1 = 7 and m= 8. DONT USE OTHER NUMBERS then your own 1. Derive the second order Taylor series expansion of the function(x) = 6 edt around x=0. Find f((k+l+ m)/10) using this approximation. Hint: Search for Leibniz Integral Rule. n! 2. For the approximation above find the upper bound on the truncation error if possible. If not possible, clearly explain why it is not possible. UPPER BOUND: (n + 1)! 3. Find the single root of function f(t) = kr + 1x2 + m2 - 1 Newton-Rhapson Method with an error tolerance of 10-5. Use initial value .ro = 1. DONT ADD your MATLAB code. 4. (USE MATLAB) Find all of the roots of function (1) = sin($)+cos(D)- using Bisection method and make sure the error is less than 10-?. On the graph, you can find some of the useful points for initialization. You can use the Bisection Method MATLAB code provided in LMS to make it compatible with this question. ADD your MATLAB code. W10 Figure 1: Graph of Jr) - Nin()+cow() - 15 K=1,L=1,M=0 1 In this assignment sometimes you will be given a question with values depending on your ID number. Assume klm is the last 3 digits. For example, if your ID number is 200205678, k = 6,1 = 7 and m= 8. DONT USE OTHER NUMBERS then your own 1. Derive the second order Taylor series expansion of the function(x) = 6 edt around x=0. Find f((k+l+ m)/10) using this approximation. Hint: Search for Leibniz Integral Rule. n! 2. For the approximation above find the upper bound on the truncation error if possible. If not possible, clearly explain why it is not possible. UPPER BOUND: (n + 1)! 3. Find the single root of function f(t) = kr + 1x2 + m2 - 1 Newton-Rhapson Method with an error tolerance of 10-5. Use initial value .ro = 1. DONT ADD your MATLAB code. 4. (USE MATLAB) Find all of the roots of function (1) = sin($)+cos(D)- using Bisection method and make sure the error is less than 10-?. On the graph, you can find some of the useful points for initialization. You can use the Bisection Method MATLAB code provided in LMS to make it compatible with this question. ADD your MATLAB code. W10 Figure 1: Graph of Jr) - Nin()+cow() - 15 K=1,L=1,M=0 1