(a) Using the first shift theorem when necessary (see below for a statement),write down the Laplace transforms of: f_{1}(t)=1-t^{3}, \quad t \geq 0 \text { ii. } f_{2}(t)=\left(1-t^{3}\right) e^{-t /

2}, \quad t \geq 0 and hence find the Laplace transform of: g(t)=\left(1-t^{3}\right)\left(1-2 e^{-t / 2}\right), \quad t \geq 0 Find constants a and b for which the inverse Laplace transform of F(s)=\frac{s+1}{2 s^{2}+\frac{1}{2}} is f(t) = a cos(t/2) + b sin(t/2), t > 0.