-173 Appendix A Solutions to the Exercises ~ ~ l u 4.4 t ~ ~ n r(t)e-’t tlt Eq 4.1: C { x ( t ) } = X ( S ) = x / 31‘ L ( A f ( t )-I-B g ( t ) }= + [ A f ( l ) L ? g ( t ) ] ~ - ’dt ~ -x S o l ~ t i ~4.5 n a) F ( s ) = ROC‘ : R e ( s } > -1 3s + + ) ( s + 1) ROC : X P { S ) > -1 b) G(s) = c) F(s) -2 + 2s - (s ) ( s + 1) +- (s 11 + G(s) = ( +5s23)(s+ 16s + a ) ( s t 1) -?- Solution 4.6 EL].4.1: G{:r(t)}= X ( ) = s i 11 - (s + 2)(s + ) ROC : 1?~{5} >