Question 3 (a) Explain why the function t) = % is not of exponential growth at most. (b) Show that, for s :9 . the Laplace transform (s) = E {i} exists. (c) Use integration by parts to show that, if g is the function in part (b), _ 1: {VG} _ 25 ' Hence, assuming that the formula cum} = 1% am} applies, show that 'lSJ _ 1 le) _ 25' Deducethat M K 9(8) = m, for some constant K. (:1) Show that, iffy is the function in part (b), [(s)12= EB (: a and hence deduce that K = Pg)