Suppose you have a quadrature Qh[f] to approximate the definite integral I[f] = Z b a f(x)dx (1) and you know that for sufficiently small h the error Eh[f] = I[f] Qh[f] satisfies Eh[f] = c4h 4 + R(h), (2) where c4 is a constant and R(h)/h4 0 as h 0. (a) What is the rate of convergence of Qh and what does it mean for the error (if h is halved what happens to the corresponding error)? (b) Use (2) to find a computable estimate of the error, E[f]. (c) Give a way to check that if h is sufficiently small for that estimate of the error to be accurate. (d) Use E[f] (or equivalently Richardson's extrapolation) to produce a more accurate quadrature from Qh.