4. (a) Let the inner product of piecewise continuous functions on the interval 0 ≤ x ≤ 3 be given by 3 (f; g) = f³ f(x)g(x) dr. L Consider three piecewise constant functions 01(x), 02(x) and 03(x): (2) Ok(x) = { 1, - if k − 1 < x < k : k = 1, 2, 3. 0, " at all other points, i. Show that 1(x), 02(x), 03(x) form an orthonormal system of functions. ii. Find the coefficients a1, a2, a3 for the best in the mean approximation of x² on the interval [0,3]. 3 f(x) = Σ akok (x) k=1 iii. On the same plot sketch graphs of the functions f(x) and x2 for 0 ≤ x ≤ 3.