April 2006 Final Solutions[1]

April 2006 Final Solutions[1] - Name:

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Sheet1 Page 1 Name: April2006Mathematics101Page2of11pagesMarks[33]1.Short-AnswerQuestions.Putyouranswerintheboxprovidedbutshowyourw Eachquestionisworth3marks,butnotallquestionsareofequaldifficulty.Fullmarkswillbegivenforacorrectanswerplacedinthebox,buta m (a)Findtheaveragevalueofcosxontheinterval[0,p]. Answer(b)Evaluate.cos2xdx. Answer(c)Evaluate. .1v1-x2+1-x2.dx. AnswerContinuedonpage3 A April2006Mathematics101Page3of11pages(d)WritedowntheSimpson„ sRuleapproximationS6for.821x2dx.Youmayleaveyouran s w Answer(e)Calculatethevolumeofthesolidobtainedbyrotatingtheregionabovethex-axis,belowthecurvey=x+x2,andbetweentheline s Answer(f)Determinethegeneralsolutionofthedifferentialequationy. .-y.-2y=0. Answer(g)Determinethegeneralsolutionofthedifferentialequationy. .-2y.+2y=0. AnswerContinuedonpage4 A April2006Mathematics101Page4of11pages(h)Aparticleismovedalongthex-axisbyaforcethatmeasuresx3/2Natapointxmfromtheo Answer(i)Determinewhether.8 1dx1+2xconvergesordiverges.Ifitconverges,evaluateit. Answer(j)Findthefirstthreenonzerotermsinthepowerseriesrepresentationinpowersofx(i.e.
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April 2006 Final Solutions[1] - Name:

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