Quiz the Last

1. Find the third order Fourier approximation to f(x) = 3x.

2. Convert {1, x} into an orthogonal set with respect to the inner product ⟨f, g⟩ = ∫_{0}^{2} f(x)g(x)dx.

3. Let L: P_{2}(x) → P_{1}(x) be given by L(p) = p′ + 2p′′. Let B = {1, x, x^{2}} be a basis for P_{2}, and let B′ = {1, x + 1} be a basis for P_{1}. Find the matrix representation of L with respect to B and B′: _{B′}[L]_{B}.