【微积分月考试卷】calculus test 1

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1、ZheJiangUniversityOfScienceAndTechnologyCivilEngineering14MiddleTestCalculusI-IIMiddleChineseTest(2015.04)NameIdClassGradeCautions:[1]Whilediscussingtheconvergenceofseries,youhavetogivethenameofthelawusedtoidentifyit.[2]Thispapercontainstwochapters:Chap11-12.

2、Ifyoucan’tfinishthissmoothly,readthebook.1.(25points)Solvethefollowingquestions,findingtheirlimitsorintegralthemtofindtheanswer.第4页共4页ZheJiangUniversityOfScienceAndTechnologyCivilEngineering14MiddleTest①②③④⑤⑥第4页共4页ZheJiangUniversityOfScienceAndTechnologyCivil

3、Engineering14MiddleTest2.(8points)ChoosingcenterforTaylorSeries,hereareseveralgivenfunctions[1]findtheconvergenceofTaylorSerieswhena=0[2]ifitisconvergent,chooseaappropriateTaylorSeriesnearthegivenfunctionofx.nearx=1.03nearx=1.003第4页共4页ZheJiangUniversityOfScie

4、nceAndTechnologyCivilEngineering14MiddleTest1.(7points)2.(20points)①②[1]Findtheseries’sradiusandintervalofconvergence[2]discussitsfunctionofsum.③Thereisaconstanta,and,pleaseshowthatf(x)converges,andfinditisconvergentconditionallyorabsolutely.④Discussthefollow

5、ingseriesdefinedbythefollowingformulasconvergence.第4页共4页ZheJiangUniversityOfScienceAndTechnologyCivilEngineering14MiddleTest1.(7points)Accordingto,calculatetheexactvalveof2.(8points)We’veknownthat,pleasefigureouttheabsolutemaximumandminimumduringtheinterval[0

6、,]3.(7points)Thereisafunction,f(x)iscontinuousatx=0[1]findf(0)[2]findthetangentlineoff(x)whenx=04.(9points)PleasefindlineL,ifitpassthroughpoint(-1,-4,-3),andisperpendicularto第4页共4页ZheJiangUniversityOfScienceAndTechnologyCivilEngineering14MiddleTest1.(9points)

7、FindtheallpossibleasymptotesofthecurveAdditional---extrabonus(10points)第4页共4页