Using l'Hopital's rule, show (this can be quite tricky) that T" (xj) lim L(x)= = x-xj 2T'(xj) Given T+1(x) = cos((n + 1) cos (x)) d dx sin((n + 1) cos(x)) Tn+1(2) = = (n + 1). T+1(k) = 1-x2 (n + 1)(1)k = 1 - x/ (1)k+j 1 - x L'(x)= = xk - 1 - x