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1、Chapter9Answers9.1（a）ThegivenintegralmaybewrittenasIf<-5,thenthefunctiongrowstowardswithincreasingtandthegivenintegraldoesnotconverge.butif>-5,thentheintegraldoesconverge(b)ThegivenintegralmaybewrittenastIf>-5,thenthefunctiongrowstowardsastdecreasestowards-andthegivenintegraldoes
2、notconverge.butif<-5,thentheintegraldoesconverge(c)ThegivenintegralmaybewrittenastClearlythisintegralhasafinitevalueforallfinitevaluesof.(d)ThegivenintegralmaybewrittenastIf>-5,thenthefunctiongrowstowardsastdecreasestowards-andthegivenintegraldoesnotconvergeIf<-5,,thenfunctiongro
3、wstowardswithincreasingtandthegivenintegraldoesnotconvergeIf=5,thentheintegralstilldoesnothaveafinitevalue.therefore,theintegraldoesnotconvergeforanyvalueof.(e)Thegivenintegralmaybewrittenast+tThefirstintegralconvergesfor<-5,thesecondinternalconvergesif>-5,therefore,thegiveninter
4、nalconvergeswhen<5.(f)ThegivenintegralmaybewrittenastIf>5,thenthefunctiongrowstowardsastdecreasetowards-andthegivenintegraldoesnotconverge.butif<5,thentheintegraldoesconverge.9.2(a)X(s)===AsshowninExample9.1theROCwillbe>-5.(b)Byusingeg.(9.3),wecaneasilyshowthatg(t)=Au(-t-)hastheL
5、aplacetransformG(s)=TheROCisspecifiedas<-5.Therefore,A=1and=-19.3UsingananalysissimilartothatusedinExample9.3weknownthatgivensignalhasaLaplacetransformoftheformX(s)ThecorrespondingROCis>max(-5,Re{}).SincewearegiventhattheROCisRe{s}>-3,weknowthatRe{}=3.therearenoconstraintsontheim
6、aginarypartof.9.4WeknowformTable9.2that,Re{s}>-1WealsoknowformTable9.1thatx(t)=X(s)=177TheROCofX(s)issuchthatifwasintheROCof,then-willbeintheROCofX(s).Puttingthetwoaboveequationstogether,wehavex(t)=(-t)=X(s)==-,<1thedenominatoroftheform-2s+5.Therefore,thepolesofX(s)are1+2jand1-2j
7、.9.5(a)thegivenLaplacetransformmaybewrittenas=.Clearly,X(s)hasazeroats=-2.sinceinX(s)theorderofthedenominatorpolynomialexceedstheorderofthenumeratorpolynomialby1,X(s)hasazeroat.Therefore,X(s)hasonezeroinfinites-planeandonezeroatinfinity.(b)ThegivenLaplancetransformmaybewrittenasX
8、(s)==Clearly,X(s)hasnozerointhefinites-p
