Need help!! For part b and second part of part c, please provide a step-by-step solution along with a detailed explanation!!!! For part a and first part of part c, please provide a step-by-step solution through the use of MALAB code along with a detailed explanation!!!! It is alright if you handwrite the step-by-step solution for part a and first part of part c but I would prefer the solution to be shown in MATLAB code. This is very URGENT!!! PLEASE reply as soon as possible!! Thank you!!

Problem 5. In this problem you will derive the barycentric weights for Chebyshev points of the second kind. Let r cos(jT), j-0,, n, and w 1 (a) In Matlab, use the formula above to evaluate u j 0, n, with 10. Verify that the weights returned by Matlab are tvo = 2n-1/(2n), wj = 2n-1 (-1)/, j = 1,. . . n _ 1, un = 2n-l (-1)"/(2n) Explain why the factor 2- can be ignored when evaluating the barycentric forula. That is, one can use, instead, the weights (b) Show that, for xj -cos(jT), and 2n-1 (r - ) lim Here Un-1()- (c) Use L'Hospital's Rule to evaluate the limt in (b) and derive the expressions in (1) sin (n arccos ) sin(arccos z) is the Chebyshev polynomial of the second kind of degree n -1 Problem 5. In this problem you will derive the barycentric weights for Chebyshev points of the second kind. Let r cos(jT), j-0,, n, and w 1 (a) In Matlab, use the formula above to evaluate u j 0, n, with 10. Verify that the weights returned by Matlab are tvo = 2n-1/(2n), wj = 2n-1 (-1)/, j = 1,. . . n _ 1, un = 2n-l (-1)"/(2n) Explain why the factor 2- can be ignored when evaluating the barycentric forula. That is, one can use, instead, the weights (b) Show that, for xj -cos(jT), and 2n-1 (r - ) lim Here Un-1()- (c) Use L'Hospital's Rule to evaluate the limt in (b) and derive the expressions in (1) sin (n arccos ) sin(arccos z) is the Chebyshev polynomial of the second kind of degree n -1