Problem: Consider the heat boundary value problem 8a $a(e_$@)$u, 00, E : 6 833 (9:13 6a u(0= t) + (1850, 13) 0, (1 + a)u(L, t) + %(L:t) = 0, M30) = 9(33), 6\" 0) 0 813(33' _ ' a) Use separation of variables and show that the corresponding Sturm Liouville problem is regular b) Determine the values of a for which the eigenvalues are nonnegative