4. Laplace Transform (20 pts) \text { i. } f(t)=t e^{-a t}\left(\sin \omega_{0} t\right)^{2} u(t) (b) The Laplace transform of a causal signal x(t) is given by X(s)=\frac{1}{s^{2}+2 s+5}, \quad

\text { ROC: } \operatorname{Re}\{s\}>-1 Which of the following Fourier transforms can be obtained from X(s) without actu-ally determining the signal x(t)? In each case, either determine the indicated Fouriertransform or explain why it cannot be determined. i. F{r(t)e¬t} ii. F{r(t)e#}