Let n 2 0 be any integer. Let x, y be any real numbers. Then the Laplace transform of the function b(t ) : = the (xtiy)t, t> 0, is the function n! B (s) : = e-stb(t) dt = S >X. o (s - (at iy) ) n+1' So the inverse Laplace transform of B(s) is the function b(t). (5) (2 marks) Let f(t), t 2 0 be any twice-derivable function such that lim e -sot f ( t ) = 0 and lim e-sotf' ( t ) = 0