Economics (a) Let T' > 0. A model in economics seeks to optimise investment M(t) by calculating a stationary path of the functional S[M] over the fixed time interval 0 0. Consider the functional Slul = dx xy?, y(a) = 0, subject to the constraint Cul = dray? = 1. (i) By using the Rayleigh-Ritz method with trial function z = z(x; A, B) = A(a2 - x2)8, where A > 0 and B > 1/2, find an approximation to the smallest eigenvalue of the associated Sturm-Liouville system. (ii) By an appropriate choice of B, find the closest approximate value of the eigenvalue from this family of trial functions