(a) With a slight change in notation the transform in (6) is the same as

With f(t) = te^at, discuss how this result in conjunction with (c) of Theorem 7.1.1 can be used to evaluate ℒ{te^at}.

(b) Proceed as in part (a), but this time discuss how to use (7) with f (t) = t sin kt in conjunction with (d) and (e) of Theorem 7.1.1 to evaluate ℒ{t sin kt}.

L{f'(1)} = sL{f(0) - f(0).