1. Let V = P₂(x) and define < f,g >= 2f (0)g(0) + f(1)g(1) +3f (2)g(2). (a) Prove that this is an inner product (You may use the fact that a quadratic poly- nomial with three roots must be zero).

Find the polynomial of least degree that interpolates the datax 3 7 1 2f(x) 10 146 2 1in(a) Lagrange form;(b) Newton form.

How large should n be to guarantee that the Trapezoidal Rule approximation to x - 12x- 48x² + 2x + 5) dæ is accurate to within 0.1. n = How large should n be to guarantee that the Simpsons Rule approximation to 2 1(-a - 12a - 48z? + 2x + 5) dx is accurate to within 0.1. n = Hint: Remember your answers should be a whole numbers, and Simpson's Rule requires even values for n Question Help: Video 1 D Video 2 Submit Question P Type here to search hp

If you know that Q(r) is a quadratic function and that Q(4) - 5, Q(9) = 2 and Q( – 10) = - 1 then: Q(x) |(2 – 4)(x – 9)(x + 10) dr