Problem $1(30\%)$ Use partial fraction expansion to find the time$-$domain waveform f$($t$)$ corresponding to the following transforms:

a$)$ F$($s$)=$

$8$

$($s$+1)($s$+3)$

Additionally, find the initial and final values of the waveforms corresponding to the

following transforms

b$)$ F$1($s$)100-$

$=$

$($s$+3)$ s$($s$+5)($s$+20)$