1) Using the definition integral (lecture notes, page 6) of Laplace transform to calculate the Laplace transform of a) f(t) = 10e-4t b) f(t) = t² 2) Use the Laplace transform tables in lecture notes on pages 17 and 18 to find the Laplace transform of each function below: a) f(t)=-10 cos 2t b) f(t)=4e3t sin(t - 45°) u(t - 45°) c) f(t)=4te-3t 3) Given that f(t) = 4e-3(-4), a) Find [] by differentiating f (t) and then using the Laplace transform tables in lecture notes on pages 18 and 19 b) Find £[f] using the theorem for differentiation dt c) Repeat a) and b) for the case that f(t) = 4e-3(-4)u(t - 4)