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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)。An
2、swer()[2](2points)AssumingthatCcirclescounterclockwiselyalongx2+y2=R2forawholecircle，thenuseGreen'sformulatocalculate，Answer()2．Questionsandanswers(3questions,14.0pointsintotal)[1](3points)Trytotransferthefunctionintopowerserieswithregardto.[2](8points)
3、If，thentrytocalculatethepowerseriesofwithregardtox,andgetthevalueof.[3](3points)Isseriesconvergent，isitabsoluteconvergent？1．Evaluations(12questions,77.0pointsintotal)[1](8points)Evaluatethecurvilinearintegral，whereListhepositiveborderoftheregionroundedb
4、ythecurve
5、x
6、+
7、y
8、=1[2](5points)Transformappropriately，andtrytofindthegeneralsolutionoftheequation.[3](6points)CalculatethedoubleintegralWhereDistheregionroundedbyxy=2,y=1+x2andlinex=2.[4](9points)Calculate,whieLis[5](6points)Proof(2xcosy－y2sinx)dx+(2ycos
9、x－x2siny)dyisthetotaldifferentialofafunction，andfindoneofitsoriginalfunction.[6](6points)Findthesolutionofthedifferentialsolutionwithregardtotheinitialconditionsgiven：[7](7points)Findthegeneralsolutiontothedifferentialequation.[8](6points)SupposeListhea
10、rchfromthroughtoalong，calculatethecurvilinearintegral.[9](8points)Calculatethelinearintegral,whileLispartoftheHyperbolicplanespiralfromto[10](2points)Findthegeneralsolutiontothedifferentialequation[11](6points)Supposef(t)isderivableatt=0,continueon[－1,1
11、]，andf(0)=0,trytocalculate。[12](8points)Findthesolutionofthedifferentialequationwithregardto.1．Proof(1question,2.0pointsintotal)[1](2points)Supposeseriesis，provethatitisdiverse.2．Trueorfalse(1question,2.0pointsintotal)[1](2points)Usedefinitiontoprovewhe
12、therseriesisdiverseorconvergent.Ifitisconvergent,findthesum.====================Answers====================Thereare19questionsinthesheet,with100pointsintotal.i.MultipleChoices(2questions,5.0pointsintotal)(3points)[1][Answer](D)(2
