Need help!! I only need part b and part c!! Please provide a step-by-step solution, along with detailed explanations, for these two parts!! This is VERY URGENT!! Please reply as soon as possible!!! Please help me!! 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