Compute the L2 norm and the sup-norm of the following functions in the interval indicated: (a) u(x) = sin πx − x, on 0 ≤ x ≤ 1 (b) u(x) = x 1/3 , on 0 ≤ x ≤ 1 (c) u(x) = cos πx + 2x − 1, on 0 ≤ x ≤ 1...

Compute the L2 norm and the sup-norm of the following functions in the interval indicated:

(a) u(x) = sin πx − x, on 0 ≤ x ≤ 1

(b) u(x) = x 1/3 , on 0 ≤ x ≤ 1

(c) u(x) = cos πx + 2x − 1, on 0 ≤ x ≤ 1

(d) u(x) = √ 1 + x2, on 0 ≤ x ≤1