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April 2007 Final Solutions[1]

April 2007 Final Solutions[1] - Name...

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Sheet1 Page 1 Name: April2007Mathematics101Page2of11pagesMarks[33]1.Short-AnswerQuestions.Putyouranswerintheboxprovidedbutshowyourw Eachquestionisworth3marks,butnotallquestionsareofequaldifficulty.Fullmarkswillbegivenforcorrectanswersplacedinthebox,buta (a)Evaluate.(2y+1)5dy. Answer(b)Evaluate.0-1(2x-ex)dx. Answer(c)Expresslimn.8 n.i=1i4n5asadefiniteintegral.Donotevaluatethisintegral. AnswerContinuedonpage3 A April2007Mathematics101Page3of11pages(d)WritedowntheSimpson¶ sRuleapproximationS4for.4011+x3dx.Youmayleaveyour Answer(e)Calculatethevolumeofthesolidobtainedbyrotatingtheregionabovethex-axis,belowthecurvey=(sinx)/x,andbetweentheli Answer(f)Writetheformofthepartial-fractiondecompositionfor10(x+1)2(x2+9) Donotdeterminethenumericalvaluesofthecoefficients. Answer(g)AnexponentiallydistributedcontinuousrandomvariableXhasprobabilitydensityfunc- tionf(x)=ke-kx,forx=0,wherekisapositiveconstant.ThemedianvalueofXequals10.Findk.
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