Show that the Chebyshev polynomials are orthogonal on ( − 1 , 1 ) (−1, 1) (−1,1) with respect to the weight function ( 1 − x 2 ) − 1 / 2 (1 − x^2)^{−1/2} (1−x2)−1/2. Ans: T n ( x ) = cos ⁡ ( n arcc

Attempt these exercises in advance of the tutorial in Week 3 Find the best L ∞ L_\infin L∞​ approximation to f ( x ) = x n + 1 + ∑ k = 0 n a k x k f (x) = x^{n+1} + \sum_{k=0}^na_kx^k f(x)=xn+1+∑k=