英文版微积分.ppt

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1、Review一、DeterminewhethertheseriesisconvergentordivergentInfiniteSequencesandSeries二、FindtheradiusofconvergenceandintervalofConvergenceofthefollowingseries.二、Findthesumofthefollowingseries.二、Findthesumofthefollowingseries.二、Findthesumofthefollowingseries.二、FindthesumofthefollowingseriesandtheMacla

2、urinSeriesforthesum.Asequenceisdefinedrecursivelybytheequation,,Determinewhethertheseriesisconvergentordivergent.Andfindthesumofthisseries.ExampleExample(19)求幂级数的收敛域及和函数.(9)若级数收敛,则级数()(A)收敛(B)收敛(C)收敛(D)收敛(19)(本题满分9分)设级数的和函数为S(x).求：(I)S(x)所满足的一阶微分方程；(II)S(x)的表达式.求幂级数的和函数f(x)及其极值.Trueorfalse1.2.3.I

3、f,thenisconvergent.Ifisdivergent,thenisdivergent.Ifforall,andisdivergent,thenisdivergent.4.Ifandconverges,thenTrueorfalse5.Ifthenisconvergent.6.Ifandconverges,thenisconvergent.Choosethebestanswerforeachofthefollowing1.IfthenA.B.C.D.Diverges2.Wehavethefollowingfourstatement:(1).Ifisconvergent,then

4、isconvergent.(2).Ifisconvergent,thenisconvergent.(3).If,thenisdivergent.(4).Ifisconvergent,thenarebothconvergent.ThenthecorrectstatementisA.(1)(2)B.(2)(3)C.(3)(4)D.(4)(1)四、Fillintheblanks:1.Ifdivergeswhenthenandconvergesat2.ThesumofisExample1.Provethat2.SupposethatShowthattheconvergenceofimpliest

5、heconvergenceof.Istheconversetrue，proveitorgiveacounter-example.1.Ifcalculateand2.IfcalculateandIfistheanglebetweenthenonzerovectorsandthenVectorsandGeometryofSpaceDirectionAnglesandDirectionCosinsThedirectionanglesofanonzerovectoraretheanglesand,thatmakeswiththepositiveandz-axes.oandarecalledthe

6、directiocosinofWehaveThevectorisaunitvectorinthedirectionofExampleFindthescalarprojectionandthevectorprojectionofontoSolutionThescalarprojectionisThevectorprojectionisThelengthofthecrossproductisequaltotheareaoftheparallelogramdeterminedbyandPropertiesofthecrossproductpærə'leləgræmThevolumeofthep

7、arallelepipeddeterminedbythevectorandisthemagnitudeoftheirscalartripleproduct:PartialDerivatives1.Ifcalculateand2.IfcalculateandChainruleShowthatwhenLaplace’sequationExampleiswritteninsphericalcoordinates,itbecomesImpl