高等数学大学英语综合模拟题

中国地质大学(北京)继续教育学院现代远程学历教育2013年春季入学测试《高等数学、大学英语》综合模拟题高等数学部分：一、选择题：在每小题给出的四个选项中，只有一项是符合题目要求的.1.极限220ln1limxxx（B）A.12B.1C.2D.e2.若2)(2xexf，则)0('f（C）A.1B.eC.2D.2e3.设函数)3)(2)(1()(xxxxxf，则)0('f等于（B）A．0B．6C．1D．34.设()，则()等于（C）A.122𝐶B.x22𝐶C.ex𝐶D.exe2x2𝐶5．设,2sinxey则dy（B）A．xdex2sinB．xdex2sinsin2C．xxdexsin2sin2sinD．xdexsin2sin6.若事件A发生必然导致事件B发生，则事件A和B的关系一定是（A）A.A⊂BB.A⊃BC.对立事件D.互不相容事件7.极限xxxxxcoscoslim(A)A．等于1B．等于0C．为无穷大D．不存在8.设',)(',)()(yxfeefyxfx则存在且=(C)A．)()()()('xfxxfxeefeefB．)(')(')(xfeefxfxC．)(')()(')()(xfeefeefxfxxfxxD．)()('xfxeef二、填空题：把答案填在题中的横线上.9.设函数2,||1(),1,||1xfxx则f[f(1)]=.10.已知33lim1nknen，则k=.11.曲线y=3x5-5x4+4x-1的拐点是.12.函数()arctanfxxx在闭区间[-1,1]上的最大值是.13.设函数e2x，则(1)|x.14.∫12(2x).15.若()＝ex则∫()1.16.已知()22，则2()x.9.110.-911.(1,1)12.4413.1;14.12taC;15.12(e2)16.1.三、解答题：解题应写出推理、演算步骤.17.计算1lnexxdx.18.设()的一个原函数为ata，求∫2().19.设函数√2，求|x1.20.设函数z=xy+f(u)，u=y2-x2，其中f是可微函数.证明：22zzyxxyxy.21.求nxmxxsinsinlim，其中nm,为自然数.22.甲、乙两袋装有大小相同的红球和白球，甲袋装有2个红球，2个白球；乙袋装有2个红球，n个白球.由甲，乙两袋中各任取2个球.（Ⅰ）若n=3，求取到的4个球全是红球的概率；（Ⅱ）若取到的4个球中至少有2个红球的概率为43，求n.23.求由曲线2及围成的平面图形的面积S以及此平面图形绕x轴旋转一周所得旋转体的体积x.参考答案：17.解：2111lnln2eexxdxxdx211ln122eexxxdx221124eex2144e18.解：因为()＝(ata)11x2，所以∫2()∫22∫(2)ataC19.解：因为＝12√x2x(1x)2x212x√x2x所以|x1220.解：证明：z()(2)yfuxx，()(2)zxfuyy2222=2()2()=zzyxyxyfuxxyfuxyxy左边右边21.解：令,xtnmnntmmtnxmxnmtx)1()sin()sin(limsinsinlim022.解：（I）记“取到的4个球全是红球”为事件A.22222245111().61060CCPACC（II）记“取到的4个球至多有1个红球”为事件B，“取到的4个球只有1个红球”为事件1B，“取到的4个球全是白球”为事件2B.由题意，得31()1.44PB2111122222122224242()nnnnCCCCCCPBCCCC22;3(2)(1)nnn22222242()nnCCPBCC(1);6(2)(1)nnnn所以,12()()()PBPBPB22(1)3(2)(1)6(2)(1)nnnnnnn14，化简，得271160,nn解得2n，或37n（舍去），故2n.23.求由曲线2及围成的平面图形的面积S以及此平面图形绕x轴旋转一周所得旋转体的体积x.解:由已知曲线画出平面图形如图所示的阴影区域.由{2，得交点坐标为（1，1）,则∫[(2)()]1(2)|1x∫(2)21∫()2112∫(2)1∫(2)112()|1(2)|121√12(1,1)-112Ox大学英语部分：Ⅰ.PhoneticsDirections:Ineachofthefollowinggroupsofwords,therearefourunderlinedlettersorlettercombinationsmarkedA,B,CandD.Comparetheunderlinedpartsandidentifytheonethatisdifferentfromtheothersinpronunciation.MarkyouranswerbyblackeningthecorrespondingletterontheAnswerSheet.l.A.backgroundB.althoughC.blouseD.amountB2.A.civilB.curriculumC.crystalD.countryA3.A.groundB.countryC.thousandD.foundB4.A.pourB.hourC.courseD.fourBⅡ.VocabularyandStructureDirections:Thereare10incompletesentencesinthissection.ForeachsentencetherearefourchoicesmarkedA,B,CandD.ChooseoneanswerthatbestcompletesthesentenceandblackenthecorrespondingletterontheAnswerSheet.5.Humanbeingsshouldfindanew_______ofenergy.BA.orientB.sourceC.originD.souse6.Thecouchiscomfortableto_______.DA.sitB.besatC.sittedD.siton7.Soloudly_______thatallthepeopleintheroomgotafright.CA.heshoutedB.shoutheC.didheshoutD.hedidshout8.Themountainis1,000feet_______thesealevel.CA.overB.higherC.aboveD.high9.Itwasa________room,withbeautifulwallpaper,waxedfloorandnicefurniture.BA.pleasedB.pleasantC.pleasingD.preasant10.Heregretted_______thedecisiontoohastily.CA.makeB.tomakeC.makingD.havemaked11.Theprofessorinsistedthatwe_______ourhomeworkbeforenextmonth.CA.handedinB.willhandinC.handinD.musthandin12.WhenIwasachildIused____swimminginthelake.CA.togoingB.goingC.togoD.go13.Saul’sbrotherleftthematterentirelyupto____and____.DA.I,heB.him,IC.me,heD.him,me14.The19thwinterGames,heldinSaltLakeCity,____anOlympictraditionwhichgoesbackalmost3,000years.DA.isthepartofB.arethepartofC.ispartofD.arepartofⅢ.ClozeDirections:Foreachblankinthefollowingpassage,therearefourchoicesmarkedA,B,CandD.ChoosetheonethatismostsuitableandmarkyouranswerbyblackeningthecorrespondingletterontheAnswerSheet.ThemostextraordinarydreamIeverhadwasoneinwhichIfanciedthat,asIwasgoingintoatheater,thecloak-roomattendant__15__Meinthelobbyandinsistedonmy__16__mylegsbehind.Iwasnotsurprised;butIwasconsiderablyannoyed.IsaidIhad__17__heardofsucharuleatanyrespectabletheater__18__,andthatIconsidereditamostabsurdregulation.Themanrepliedthathewasvery__19__,butthatthosewerehisinstructions.Peoplecomplainedthattheycouldnotgettoandfromtheir__20__comfortably,becauseotherpeople’slegswerealwaysinthe__21__;andithad,therefore,beendecidedthat__22__shouldleavetheirlegoutside.Itseemedtomethatthemanagement,inmakingthisorder,hadgone__23__theirlegalright;and,underordinarycircumstances,Ishouldhavedisputedit.However,Ididn’twantto__24__adisturbance;and__25__Isatdownandmeeklypreparedtocomplywiththedemand.Ihadneverbefore__26__thatthehumanlegcouldbeunscrewed.Ihadalways__27__itwasmoresecurelyfixed.Butthemanshowedmebowtoundothem,andIfoundthattheycameoff__28__easily.Thediscoverydidnotsurprise__29__anymorethantheoriginalrequestthatIshouldtakethemoff.Nothingdoessurpriseoneinadream.15.A.calledB.helpedC.stoppedD.metC16.A.leaveB.leavesC.leavingD.leftC17.A.everB.neverC.onceD.alwaysB18.A.beforeB.afterC.duringD.behindA19.A.angryB.sorryC.friendlyD.helpfulB20.A.homesB.jobsC.armsD.seatsD21.A.roadB.lobbyC.theaterD.wayD22.A.somebodyB.everybodyC.anybodyD.nobodyB23.A.beyondB.fromC.toD.aroundA24.A.understandB.mak