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设w=fxy·gx+hxy其中fgh均为可微函数则等于
f
′·g+f·g′+h
′
f
′·g′+h
′
f·g′+h
′
以上三个结论都不正确
设fxgx为连续可微函数且存在uxy使得du=yfxydx+xgxydy求fx-gx.
设y=flnxefx其中f可微则dy=
设函数fg均可微z=fxylnx+gxy则=
设其中fg均可微则
设fg均可微z=fxylnx+gxy则.
设函数f与g均可微z=fxylnx+gxy则=______.
设fg均可微z=fxylnz+gxy则=______
设其中fgψ在其定义域内均可微求
设其中fg均可微则
设fxgx为连续可微函数且ω=yfxydx+xgxydy.若存在u使得du=ω求f-g
设函数fxgx在[ab]上均可导且f′x<g′x则当a<x<b时有
f(x)>g(x)
f(x)+g(a)<g(x)+f(a)
f(x)<g(x)
f(x)+g(b)<g(x)+f(b)
设y=fxt而t是由方程Gzyt=0确定的xy的函数其中fxtGxyt为可微函数求[*].
设其中fg均可微则=
设函数fuv由关系式f[xgyy]=x+gy确定其中函数gy可微且gy≠0则=
设单调可微函数fx的反函数为gxf1=3f′1=2f″3=6则g′3=
设fxgx可微且f’x=gxg’x=-fxf0=0f’0=1证明f2x+g2x=1.
设其中fg均可微则
设其中fgφ在其定义域内均可微求.
设其中f与g均可微则=
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设方程组确定隐函数y=yx与z=zx且y1=1z1=0则y’1+2z’1=______.
Directions:Atpresentmuchattentionisbeingattachedtotheenvironmentalprotection.Writealettertoadvocatecar-pooling.Andinyourletteryoushouldatleaststatetheaimofyourwritingandtheadvantagesofcar-pooling.Youshouldwriteabout100wordsonANSWERSHEET2.Donotsignyourownnameattheendoftheletter.UseLiMinginstead.Youdonotneedtowritetheaddress.
设a为常数则数列极限=______.
设多项式Pnx在x=1处有等于6的极大值在x=3处有等于2的极小值则其中次数n最低的多项式Pnx=______.
[A]DrDanielStanleyanoceanographerhasfoundvolcanicshardsinEgyptthathebelievesarelinkedtotheexplosion.ComputersimulationsbyMikeRampinoaclimatemodelerfromNewYorkUniversityshowthattheresultingashcloudcouldhaveplungedtheareaintodarknessaswellasgeneratinglightningandhailtwoofthe10plagues. [B]Thecloudcouldhavealsoreducedtherainfallcausingadrought.IftheNilehadthenbeenpoisonedbytheeffectsoftheeruptionpollutioncouldhaveturneditredashappenedinarecentenvironmentaldisasterinAmerica.Thesamepollutioncouldhavedrivenmillionsoffrogsontothelandthesecondplague.Onlandthefrogswoulddieremovingtheonlyobstacletoanexplosionoffliesandlice—thethirdandfourthplagues.Thefliescouldhavetransmittedfataldiseasestocattlethefifthplagueandboilsandblisterstohumansthesixthplague. [C]MoseswhichwillbebroadcastinDecember2002willsuggestthatmuchoftheBiblestorycanheexplainedbyasinglenaturaldisasterahugevolcaniceruptionontheGreekislandofSantoriniinthe16thcenturyBC. [D]Thehour-longdocumentaryarguesthateventhestoryofthepartingoftheRedSeawhichallowedMosestoleadtheHebrewstosafetywhilethepursuingEgyptianarmywasdrownedmayhaveitsoriginsintheeruption.Itrepeatsthetheorythat"RedSea"isamistranslationoftheSeaofReedsamuchshallowerswamp. [E]TheprogrammetellsthestoryofhowMosesledtheHebrewsoutofEgyptafteraseriesofplagueshaddevastatedthecountry.Butitalsousesnewscientificresearchtoarguethatmanyoftheeventssurroundingtheexoduscouldhavebeentriggeredbytheeruptionwhichwouldhavebeenathousandtimesmorepowerfulthananuclearbomb. [F]ComputersimulationsshowthattheSantorinieruptioncouldhavetriggereda600ft-hightidalwavetravelingatabout400milesanhourwhichwouldhavebeen6fthighandahundredmileslongwhenitreachedtheEgyptiandelta.Suchaneventwouldhavebeenrememberedforgenerationsandmayhaveprovidedtheinspirationforthestory. [G]FreshevidencethattheBiblicalplaguesandthepartingoftheRedSeawerenaturaleventsratherthanmythsormiraclesistobepresentedinanewBBCdocumentary. Order: 41
设fx在x=0的某邻域内有定义且满足求极限
设B是3阶非零矩阵且满足BA=0.Ⅰ求矩阵BⅡ如果矩阵B的第1列是12-3T求B-E6.
求椭圆5x2+8xy+5y2=9的长短半轴之长.
设函数fx满足f'0=0f0<0则存在δ>0使得
设二元函数fuv具有二阶连续偏导数且满足又gxy=fx2-y22xy则=______.
设半径为1的球正好有一半沉入水中球的比重为1现将球从水中取出问要作多少功假设在球从水中取出的过程中水面的高度不变.
[A]DrDanielStanleyanoceanographerhasfoundvolcanicshardsinEgyptthathebelievesarelinkedtotheexplosion.ComputersimulationsbyMikeRampinoaclimatemodelerfromNewYorkUniversityshowthattheresultingashcloudcouldhaveplungedtheareaintodarknessaswellasgeneratinglightningandhailtwoofthe10plagues. [B]Thecloudcouldhavealsoreducedtherainfallcausingadrought.IftheNilehadthenbeenpoisonedbytheeffectsoftheeruptionpollutioncouldhaveturneditredashappenedinarecentenvironmentaldisasterinAmerica.Thesamepollutioncouldhavedrivenmillionsoffrogsontothelandthesecondplague.Onlandthefrogswoulddieremovingtheonlyobstacletoanexplosionoffliesandlice—thethirdandfourthplagues.Thefliescouldhavetransmittedfataldiseasestocattlethefifthplagueandboilsandblisterstohumansthesixthplague. [C]MoseswhichwillbebroadcastinDecember2002willsuggestthatmuchoftheBiblestorycanheexplainedbyasinglenaturaldisasterahugevolcaniceruptionontheGreekislandofSantoriniinthe16thcenturyBC. [D]Thehour-longdocumentaryarguesthateventhestoryofthepartingoftheRedSeawhichallowedMosestoleadtheHebrewstosafetywhilethepursuingEgyptianarmywasdrownedmayhaveitsoriginsintheeruption.Itrepeatsthetheorythat"RedSea"isamistranslationoftheSeaofReedsamuchshallowerswamp. [E]TheprogrammetellsthestoryofhowMosesledtheHebrewsoutofEgyptafteraseriesofplagueshaddevastatedthecountry.Butitalsousesnewscientificresearchtoarguethatmanyoftheeventssurroundingtheexoduscouldhavebeentriggeredbytheeruptionwhichwouldhavebeenathousandtimesmorepowerfulthananuclearbomb. [F]ComputersimulationsshowthattheSantorinieruptioncouldhavetriggereda600ft-hightidalwavetravelingatabout400milesanhourwhichwouldhavebeen6fthighandahundredmileslongwhenitreachedtheEgyptiandelta.Suchaneventwouldhavebeenrememberedforgenerationsandmayhaveprovidedtheinspirationforthestory. [G]FreshevidencethattheBiblicalplaguesandthepartingoftheRedSeawerenaturaleventsratherthanmythsormiraclesistobepresentedinanewBBCdocumentary. Order: 43
设函数φx可导且满足φ0=0又φ’x单调减少.Ⅰ证明对x∈01有φ1x<φx<φ’0xⅡ若φ1≥0φ’0≤1任取x0∈01令xn=φxn-1n=12证明存在并求出该极限.
Companieshaveembarkedonwhatlookslikethebeginningsofare-runofthemergersandacquisitionsM&Awavethatdefinedthesecondbubblyhalfofthe1990s.Thatperiodreadersmightrecallwascharacterizedbyacollectivesplurgethatsawthecreationofsomeofthemostindebtedcompaniesinhistorymanyofwhichlaterwentbankruptorwerethemselvesbrokenup.WildbiddingfortelecomsinternetandmediaassetsnottomentionthemadnessthatwasDaimler’s$40billionmotoringtakeoverin1998-1999ofChryslerortheTime-Warner/AOLmega-mergerin2000helpedtogivemergersathoroughlybadname.AconsensusemergedthatM&Awasagreatwayforinvestmentbankstoreaprichfeesandasurewayforambitiousmanagerstobetrayinvestorsbytrashingthevalueoftheirshares.NowM&Aisback.ItsreturnisaglobalphenomenonbutitisperhapsmoststrikinginEuropewheresofarthisyeartherehasbeenastreamofdealsworthmorethan$600billionintotalaround40%higherthaninthesameperiodof2004.ThelatesteffortcamethisweekwhenFrance’sSaint-Gobainabuilding-materialsfirmunveiledthedetailsofits£3.6billion$6.5billionhostilebidforBPBaBritishrival.Inthefirsthalfoftheyearcross-borderactivitywasupthreefoldoverthesameperiodlastyear.EvenFranceTelecomwhichwasleftalmostbankruptattheendofthelastmergerwaverecentlyboughtAmenaaSpanishmobileoperator.Shareholder’sapprovalofallthesedealsraisesaninterestingquestionforcompanieseverywhere:areinvestorsrighttothinkthinthesemergersaremorelikelytosucceedthanearlieronesTherearetwoanswers.Thefirstisthatpastmergersmayhavebeenjudgedtooharshly.ThesecondisthatthepresentrashofEuropeandealsdoeslookmorerationalbut—andthecaveatiscrucial—onlysofar.Thepatternmaynothold.M&A’spoorreputationstemsnotonlyfromthestringofspectacularfailuresinthe1990sbutalsofromstudiesthatshowedvaluedestructionforacquiringshareholdersin80%ofdeals.Butmorerecentstudiesbyeconomistshaveintroducedanoteofcaution.Investorsshouldlookatthenumberofdealsthatsucceedorfailtypicallymeasuredbytheimpactonthesharepriceratherthanasyoumightthinkweighingthembysize.ForexamplenoonedoubtsthattheDaimler-Chryslermergerdestroyedvalue.ThecombinedmarketvalueofthetwofirmsisstillbelowthatofDaimleralonebeforethedeal.ThissingledealaccountedforhalfofallGermanM&Aactivitybyvaluein1998and1999andprobablydominatedpeople’sthinkingaboutmergerstothesamedegree.Throwinafewothersuchmonstersanditisnowonderthatbroadstudieshavetendedtofindthatmergersareabadidea.Thetruepictureismorecomplicated.Thepatterninthethirdparagraphmostprobablydenotes______.
曲线在t=0对应点处切线的直角坐标方程是______.
求常数k的取值范围使得不等式kln1+x>arctanx当x>0时成立.
作自变量替换把方程变换成y关于t的微分方程并求原方程的通解.
Inthepastyearalothaschangedinthefieldofhumanspaceflight.46InJanuaryPresidentGeorgeBushbrushedasidethefactthatAmerica’sentirespace-shuttlefleetwasgroundedwhenheannouncedgrandioseplanstoputpeoplebackonthemoonandthentolaunchamannedmissiontoMars.47InJuneButtRutananAmericanaeronauticalengineershowedthathumanspaceflightwasnolongerthepreserveofgovernmentsbysendingamantotheedgeofspaceinSpaceShipOneaprivatelyfinancedvehiclethatcostaboutthesametobuildasaluxuryyacht.ThatwasfollowedinSeptemberbySirRichardBransontheBritishentrepreneurbehindtheVirginbrandannouncingthathehadsignedadealwithMrRutantoworkonplansforafleetoffivesuborbitalvehiclesdevelopedfromSpaceShipOne. 48NowinthedyingdaysoftheyearAmerica’sCongresshaspassedabillthatunravelsatangleaboutwhowouldberesponsibleforregulatingthefledglingindustryandunderwhatterms.49ThebillalsoallowspassengerstoflyontheunderstandingthatthisnewgenerationofvehiclesmaynotbeassafeastakingacommercialflightbetweensayNewYorkandLondon. TheofficiallinefromVirginGalacticaasSirRichard’slatestventureismodestlynamedisthatthiscomingchangeinthelawmakesnopracticaldifferencetothefirm’splanssincetheydonotintendtoflyunlesstheycanmaketheirspacecraftassafeasaprivatejet.Butitmustsurelycomeassomesortofrelief.InanycaseWillWhitehorndirectorofcorporateaffairsatVirgin’sheadquartersinLondonandsoontobecomethepresidentofVirginGalacticasaysthatworkisunderwayonamockupoftheinteriorofanewspacecraftthatwillholdfivepassengers.50Virginhasalreadycommitted$20mtowardslicensingtheSpaceShipOnetechnologyfromMr.RutanandhisfinancialbackerPaulAllenasoftwarebillionaire. 49
设fx在[0+∞连续在0+∞可导x∈0+∞时fx>0且单调上升x=gy为y=fx的反函数它们满足则fx的表达式是______.
Apairofdicerolledagainandagainwilleventuallyproducetwosixes.Similarlythevirusthatcausesinfluenzaisconstantlychangingatrandomandonedaywillmutateinawaythatwillenableittoinfectbillionsofpeopleandtokillmillions.Manyexpertsnowbelieveaglobaloutbreakofpandemicfluisoverdueandthatthenextonecouldbeasbadastheonein1918whichkilledsomewherebetween25mand50mpeople.Todayhoweveradvancesinmedicineofferrealhopethatanothersuchoutbreakcanbecontained—ifgovernmentsstartpreparingnow.Newresearchpublishedthisweeksuggeststhatarelativelysmallstockpileofanantiviraldrug—aslittleas3mdoses—couldbeenoughtolimitsharplyaflupandemicifthedrugsweredeployedquicklytopeopleintheareasurroundingtheinitialoutbreak.Thedrug’smanufacturerRocheistalkingtotheWorldHealthOrganisationaboutdonatingsuchastockpile.Thisisgoodnews.ButmuchmoreneedstobedoneespeciallywithanastystrainofavianfluspreadinginAsiawhichcouldmutateintoathreattohumans.SincetheSARSoutbreakin2003afewcountrieshavedevelopedplansinpreparationforsimilarepisodes.Butprogresshasbeenshamefullypatchyandthereisstillfartoolittleinternationalcoordination.Aglobalstockpileofdrugsalonewouldnotbemuchusewithoutanadequatesystemofsurveillancetoidentifyearlycasesandawayofdeliveringtreatmentquickly.Ifanoutbreakoccurredinaborderregionforexampleaswiftresponsewouldmostlikelydependonprioragreementsbetweendifferentcountriesaboutquarantineandcontainment.Reachingsuchagreementsisrarelyeasybutthatmakesthetaskallthemoreurgent.Richcountriestendtobebetterpreparedthanpooronesbutthisshouldbenoconsolationtothem.Fludoesnotrespectborders.Itisineveryone’sinteresttomakesurethatdevelopingcountriesespeciallyinAsiaarealsowellprepared.Manymaybridleatinterferencefromoutside.Butifrichernationswerewillingtodonateanti-viraldrugsandguaranteeasupplyofanyvaccinethatbecomesavailablepoorernationsmightbewillingtoreachagreementsoversurveillanceandpreparedness.Simplysortingoutafewdetailsnowwillhavelivesandrecriminationslater.WilltherebeenoughventilatorsmakesanddrugsWherewillpeoplebetreatedifthehospitalsoverflowWillfoodbedeliveredasnormalToomanycountrieshavenoanswerstothesequestions.Thebesttitleforthetextwouldbe______.
=______.
设fx在[01]上连续在01内二次可导且fx在[01]上的最大值M=2最小值m=0求证若fx的最大值点或最小值点至少有一个是区间01内的点则在01内必存在两点ξ与η使得|f’ξ|>2|fη|>4成立.
确定常A与b的值使得
若f-10为函数fxy=e-xax+b-y2的极大值则常数ab应满足的条件是______.
Companieshaveembarkedonwhatlookslikethebeginningsofare-runofthemergersandacquisitionsM&Awavethatdefinedthesecondbubblyhalfofthe1990s.Thatperiodreadersmightrecallwascharacterizedbyacollectivesplurgethatsawthecreationofsomeofthemostindebtedcompaniesinhistorymanyofwhichlaterwentbankruptorwerethemselvesbrokenup.WildbiddingfortelecomsinternetandmediaassetsnottomentionthemadnessthatwasDaimler’s$40billionmotoringtakeoverin1998-1999ofChryslerortheTime-Warner/AOLmega-mergerin2000helpedtogivemergersathoroughlybadname.AconsensusemergedthatM&Awasagreatwayforinvestmentbankstoreaprichfeesandasurewayforambitiousmanagerstobetrayinvestorsbytrashingthevalueoftheirshares.NowM&Aisback.ItsreturnisaglobalphenomenonbutitisperhapsmoststrikinginEuropewheresofarthisyeartherehasbeenastreamofdealsworthmorethan$600billionintotalaround40%higherthaninthesameperiodof2004.ThelatesteffortcamethisweekwhenFrance’sSaint-Gobainabuilding-materialsfirmunveiledthedetailsofits£3.6billion$6.5billionhostilebidforBPBaBritishrival.Inthefirsthalfoftheyearcross-borderactivitywasupthreefoldoverthesameperiodlastyear.EvenFranceTelecomwhichwasleftalmostbankruptattheendofthelastmergerwaverecentlyboughtAmenaaSpanishmobileoperator.Shareholder’sapprovalofallthesedealsraisesaninterestingquestionforcompanieseverywhere:areinvestorsrighttothinkthinthesemergersaremorelikelytosucceedthanearlieronesTherearetwoanswers.Thefirstisthatpastmergersmayhavebeenjudgedtooharshly.ThesecondisthatthepresentrashofEuropeandealsdoeslookmorerationalbut—andthecaveatiscrucial—onlysofar.Thepatternmaynothold.M&A’spoorreputationstemsnotonlyfromthestringofspectacularfailuresinthe1990sbutalsofromstudiesthatshowedvaluedestructionforacquiringshareholdersin80%ofdeals.Butmorerecentstudiesbyeconomistshaveintroducedanoteofcaution.Investorsshouldlookatthenumberofdealsthatsucceedorfailtypicallymeasuredbytheimpactonthesharepriceratherthanasyoumightthinkweighingthembysize.ForexamplenoonedoubtsthattheDaimler-Chryslermergerdestroyedvalue.ThecombinedmarketvalueofthetwofirmsisstillbelowthatofDaimleralonebeforethedeal.ThissingledealaccountedforhalfofallGermanM&Aactivitybyvaluein1998and1999andprobablydominatedpeople’sthinkingaboutmergerstothesamedegree.Throwinafewothersuchmonstersanditisnowonderthatbroadstudieshavetendedtofindthatmergersareabadidea.Thetruepictureismorecomplicated.Theconclusionreachedbygeneralresearchesisthatmergersarenot______.
设αβ都是n维非零列向量矩阵A=2E-αβT其中E是n阶单位矩阵.若A2=A+2E则αTβ=______.
设A是n阶反对称矩阵Ⅰ证明A可逆的必要条件是n为偶数当n为奇数时A*是对称矩阵Ⅱ举一个4阶不可逆的反对称矩阵的例子Ⅲ证明如果λ是A的特征值那么-λ也必是A的特征值.
求累次积分.
Inthepastyearalothaschangedinthefieldofhumanspaceflight.46InJanuaryPresidentGeorgeBushbrushedasidethefactthatAmerica’sentirespace-shuttlefleetwasgroundedwhenheannouncedgrandioseplanstoputpeoplebackonthemoonandthentolaunchamannedmissiontoMars.47InJuneButtRutananAmericanaeronauticalengineershowedthathumanspaceflightwasnolongerthepreserveofgovernmentsbysendingamantotheedgeofspaceinSpaceShipOneaprivatelyfinancedvehiclethatcostaboutthesametobuildasaluxuryyacht.ThatwasfollowedinSeptemberbySirRichardBransontheBritishentrepreneurbehindtheVirginbrandannouncingthathehadsignedadealwithMrRutantoworkonplansforafleetoffivesuborbitalvehiclesdevelopedfromSpaceShipOne. 48NowinthedyingdaysoftheyearAmerica’sCongresshaspassedabillthatunravelsatangleaboutwhowouldberesponsibleforregulatingthefledglingindustryandunderwhatterms.49ThebillalsoallowspassengerstoflyontheunderstandingthatthisnewgenerationofvehiclesmaynotbeassafeastakingacommercialflightbetweensayNewYorkandLondon. TheofficiallinefromVirginGalacticaasSirRichard’slatestventureismodestlynamedisthatthiscomingchangeinthelawmakesnopracticaldifferencetothefirm’splanssincetheydonotintendtoflyunlesstheycanmaketheirspacecraftassafeasaprivatejet.Butitmustsurelycomeassomesortofrelief.InanycaseWillWhitehorndirectorofcorporateaffairsatVirgin’sheadquartersinLondonandsoontobecomethepresidentofVirginGalacticasaysthatworkisunderwayonamockupoftheinteriorofanewspacecraftthatwillholdfivepassengers.50Virginhasalreadycommitted$20mtowardslicensingtheSpaceShipOnetechnologyfromMr.RutanandhisfinancialbackerPaulAllenasoftwarebillionaire. 47
[A]DrDanielStanleyanoceanographerhasfoundvolcanicshardsinEgyptthathebelievesarelinkedtotheexplosion.ComputersimulationsbyMikeRampinoaclimatemodelerfromNewYorkUniversityshowthattheresultingashcloudcouldhaveplungedtheareaintodarknessaswellasgeneratinglightningandhailtwoofthe10plagues. [B]Thecloudcouldhavealsoreducedtherainfallcausingadrought.IftheNilehadthenbeenpoisonedbytheeffectsoftheeruptionpollutioncouldhaveturneditredashappenedinarecentenvironmentaldisasterinAmerica.Thesamepollutioncouldhavedrivenmillionsoffrogsontothelandthesecondplague.Onlandthefrogswoulddieremovingtheonlyobstacletoanexplosionoffliesandlice—thethirdandfourthplagues.Thefliescouldhavetransmittedfataldiseasestocattlethefifthplagueandboilsandblisterstohumansthesixthplague. [C]MoseswhichwillbebroadcastinDecember2002willsuggestthatmuchoftheBiblestorycanheexplainedbyasinglenaturaldisasterahugevolcaniceruptionontheGreekislandofSantoriniinthe16thcenturyBC. [D]Thehour-longdocumentaryarguesthateventhestoryofthepartingoftheRedSeawhichallowedMosestoleadtheHebrewstosafetywhilethepursuingEgyptianarmywasdrownedmayhaveitsoriginsintheeruption.Itrepeatsthetheorythat"RedSea"isamistranslationoftheSeaofReedsamuchshallowerswamp. [E]TheprogrammetellsthestoryofhowMosesledtheHebrewsoutofEgyptafteraseriesofplagueshaddevastatedthecountry.Butitalsousesnewscientificresearchtoarguethatmanyoftheeventssurroundingtheexoduscouldhavebeentriggeredbytheeruptionwhichwouldhavebeenathousandtimesmorepowerfulthananuclearbomb. [F]ComputersimulationsshowthattheSantorinieruptioncouldhavetriggereda600ft-hightidalwavetravelingatabout400milesanhourwhichwouldhavebeen6fthighandahundredmileslongwhenitreachedtheEgyptiandelta.Suchaneventwouldhavebeenrememberedforgenerationsandmayhaveprovidedtheinspirationforthestory. [G]FreshevidencethattheBiblicalplaguesandthepartingoftheRedSeawerenaturaleventsratherthanmythsormiraclesistobepresentedinanewBBCdocumentary. Order: 45
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