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1、线订装封密题号—-四五七八九十总成绩得分阅卷教师签字：符伟张燕、Directions:Thereare5questionsinthispart.Foreachquestiontherearefour西南交通大学2010-2011学年第（二）学期考试试卷考试时间120minutes课程代码2〔00081课程名称advancecalculuschoicesmarkedA),B),C)andD).ChoosetheONEanswerthatbestcompletesthequestuion.Thenmarkthecor
2、respondingletterontheAnswerSheetwithasingleline.20Inthefollowing,theellipsoidis(++=4z2、乂；y2£"xD+x4、oCZ1□czTestdivergentofthefollowingseries()・线iT'-sl封書cos(n)2nn1,p(n'3、Changetheorderofintegration1Xdxf(x,y)dy(1ln(1Adyf(x,y)dx・Bdyf(x,y)dx・C0000dyf(x,y)dx.D01dyf
3、(x,y)dx.0y4、EvalutatelimitoffunctionA0・Be.clim(1Xy55、TheintervaIofconvergenceofseriesniS()线订装封密级A(-1,1).C[-1,1]、Directions:Thereare5questionsincorrespondingblank.5420thispart・writethecorrectsolutionintheFindthemaclaurinseriesoffunctionf(x)arctanx2、Letthefunct
4、ion_vZXoOy2,thenthetotaldifferentialdzatpoint(1,1)is3、Letf(x)xa0ancosnxn1Jin[o,],then乳,=ss4、TheIBeintegralxds(where丄is,y=x(1x3))is5、Let-isthepartofthespherex2__屮Z24withorientationtowardtheorigin,Thenxdydz3ydzdx2zdxdy22acx2xc3y三、Directions:Thereare8questionsi
5、nthispartevaluate^theAllowingquestionsandwritesteps:(7642)l--=Findatangentlineequationofcurvec2Letwf(xy,y乙zx)IJfindqW,.andwyyz3、Evaluatedoubleintegrals(2xD2y5)d訓hereDistheregionbyx2y24、・Findthesumfunctionofthefollowingseriesf+++xnn1n25、(xyz)dv,wherexsin2)(xc
6、osisboundedbyx=0,y=0,z=0andx+y+z=1./Is込)6、(eyydxeyxdy,wherecisthecirclex_+_+2.frompoint(0,2)2yyto(0,0)7、EvaluatethesurfaceintegralxyzdS,whereisthepartofthecone2x2y2zBetweenz=1andz=4.四.(9)Showthat(6xyydx3)xy2(6xy23ydy)0betotaldifferentialequationandevaluategen
7、eralsolution五、(9)Findthemaximumvolumeofarectangularboxwhosesurfaceareais15i0i0・
