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1、浙江师范大学《高等数学》(二)期末试卷(A卷)(2007—2008学年第二学期)考试形式:闭卷使用学生:初阳综合理科07级考试时间:150分钟出卷时间:2008年5月25日说明:考生应将全部答案都写在答题纸上,否则作无效处理。1.MultipleChoices(2questions,5.0pointsintotal)[1](3points)Ifseriesandarediverse,thenwhichofthefollowingseriesmustbediverse:(A);(B)(C);(D)。Answer()[2](2points)AssumingthatCcirclescounter
2、clockwiselyalongx2+y2=R2forawholecircle,thenuseGreen'sformulatocalculate,Answer()2.Questionsandanswers(3questions,14.0pointsintotal)[1](3points)Trytotransferthefunctionintopowerserieswithregardto.[2](8points)If,thentrytocalculatethepowerseriesofwithregardtox,andgetthevalueof.[3](3points)Isseriesco
3、nvergent,isitabsoluteconvergent?1.Evaluations(12questions,77.0pointsintotal)[1](8points)Evaluatethecurvilinearintegral,whereListhepositiveborderoftheregionroundedbythecurve
4、x
5、+
6、y
7、=1[2](5points)Transformappropriately,andtrytofindthegeneralsolutionoftheequation.[3](6points)Calculatethedoubleintegral
8、WhereDistheregionroundedbyxy=2,y=1+x2andlinex=2.[4](9points)Calculate,whieLis[5](6points)Proof(2xcosy-y2sinx)dx+(2ycosx-x2siny)dyisthetotaldifferentialofafunction,andfindoneofitsoriginalfunction.[6](6points)Findthesolutionofthedifferentialsolutionwithregardtotheinitialconditionsgiven:[7](7points)F
9、indthegeneralsolutiontothedifferentialequation.[8](6points)SupposeListhearchfromthroughtoalong,calculatethecurvilinearintegral.[9](8points)Calculatethelinearintegral,whileLispartoftheHyperbolicplanespiralfromto[10](2points)Findthegeneralsolutiontothedifferentialequation[11](6points)Supposef(t)isde
10、rivableatt=0,continueon[-1,1],andf(0)=0,trytocalculate。[12](8points)Findthesolutionofthedifferentialequationwithregardto.1.Proof(1question,2.0pointsintotal)[1](2points)Supposeseriesis,provethatitisdiverse.2.Trueorfalse(1question,2.0pointsintotal)[1](2points)Usedefinitiontoprovewhetherseriesisdiver
11、seorconvergent.Ifitisconvergent,findthesum.====================Answers====================Thereare19questionsinthesheet,with100pointsintotal.i.MultipleChoices(2questions,5.0pointsintotal)(3points)[1][Answer](D)(2