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设g(x)在x=0连续且满足g(x)=1+2x+o(x)(x→0),又F(x)=fg(x)],则F’(0)=______。
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设fx在0+∞内一阶连续可微且对[*]满足[*]xfx+x3又f1=0求fx.
设fx在[01]上二阶连续可导且f’0=f’1.证明存在ξ∈01使得[*]
设fx在0+∞内一阶连续可微且对满足xfx+x3又f1=0求fx.
设fx二阶连续可导且f0=0f’0=1求uxy使du=y[fx+3e2x]dx+f’xdy.
以G代表组织病理学分级可分为
Gx-4
G0-4
Gx-0
G1-4
Gx-3
设fx有二阶连续导数且z=fexsiny满足则函数fx=______
设fx在[0a]上一阶连续可导f0=0在0a内二阶可导且fx>0.证明[*]
已知x>0y>0且满足3x+2y=12则1gx+1gy的最大值为
1g6
1g3
1g12
21g
设函数fx具有三阶连续导数且满足
设函数fx在-11内具有二阶连续导数且满足f’0=1则=______.
设fx在x=0的某邻域中有一阶连续导数且f0≠0f’0≠0当h→0时afh+bf2h-f0是比h高阶
设fx在[0+∞上具有二阶连续导数且f0>0f’0<0f’’x≥k>0试确定fx在0+∞内零点的个数
设fx在[01]上二阶连续可导且f’0=f’1.证明存在ξ∈01使得
设gx在x=0连续且满足gx=1+2x+oxx→0又Fx=fgx]则F’0=______
设fx在[0a]上一阶连续可导f0=0在0a内二阶可导且fx>0.证明
设z=zxy有二阶连续偏导数且满足 Ⅰ作自变量与因变量变换u=x+yυ=x-yω=xy-z.变换
设在x=0连续且满足gx=1+2x+oxx→0.又Fx=f[gx]则F’0=______.
设fx在x=0邻域有二阶连续导数且满足f’0=1则______.
若函数fx在点x0间断gx在点x0连续则fzgx在点x0
间断
连续
第一类间断
可能间断可能连续
设函数u的全微分du=[ex+f’x]ydx+f’xdy其中f在-∞+∞内具有二阶连续的导数且f0=
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ForhealthinsurancetheUnitedStateshastakentheroadlesstraveled.TheUnitedStatesistheonlyrichcountrywithoutuniversalhealthinsurance.PeopleintheUnitedStatesspendthemostrelyheavilyontheprivatesectorandobtaincarefromtheworld’smostcomplicateddeliverysystem.WhilesomesupportershaveexpressedsatisfactionifnotprideintheseremarkablequalitiesotherscontendthattheUnitedStatesfacesuniquelimitationsinreforminghealthcare.InherexceptionalbookPartingattheCrossroadsAntoniaMaionicomparestheformationoftheU.S.andCanadianhealth-caresystemsfortheyears1930—1960.TheUnitedStatesandCanadaareoftenconsideredthemostsimilarofWesterndemocracies.Theyshareacommonborderarewealthyandhavefederalgovernment.Theirtradeunionsareonlymoderatelypowerfulandtheirpopulationsarediverseandyoung.Neverthelesstheirheath-insurancesystemsarenearlyopposite.TheUnitedStatesreliesonamixofgovernmentplans.TargetedtotheelderlyandindigentandemploymentbasedplanswhichthegovernmentindirectlysupportsCanadaofferspublichealthinsurancetoallqualifiedresidentwiththeprivatesectorprovidingsupplementaryservicesinsomeprovinces.Labororganizationsbecamestrongadvocatesforhealth-insurancereforminbothcountries.Theirimpactpartiallydependedonpoliticalinstitutionsandhowotheractorsparticularlyorganizedmedicinewieldedthem.Canada’sgovernmentalandelectoralsystemsallowedlabortocooperatewithasocialdemocraticpartyintheSaskatchewanprovincewhichestablishedauniversalprogram.TheSaskatchewanprogramdemonstrateduniversalinsurancefeasibilityspurringthedominantLiberalstointroduceanationaluniversalprogram.IncontrasttheU.S.electoralsystemeffectivelyprecludedthird-partyformationforcingorganizedlabortodiluteitshealth-insurancegoalsbecauseitwasoneofmanyinterestsrepresentedbytheDemocraticParty.Maionisuggeststhateconomicvitalityisimportantforthefutureofbothcountries’systemsbuttheprognosisisuncertain.DespiterecentconcernsabouttheCanadiangovernment’sbudgetaryhealthMaionicontendsthatwidespreadsupportprotectsuniversalinsurance.ConverselyMaioniseemspessimisticaboutoptionsforU.S.universalhealthinsurance.Despiteeconomicbuoyancydissensionwilllikelypreventreforms.AlthoughadevastatingeconmnicdownturnwouldmakehealthfinancedifficultineithercountrytheU.S.systemseemsespeciallyvulnerable.Employment-basedinsuranceandMedicarebothrelyonlabormarketattachment.HighchronicunemploymentcouldresultincoveragelossandfinancialdifficultiesforemployerinsuranceandMedicareswellingtheuninsuredpool.Suchacrisiscouldprovideanopeningforuniversalhealthinsurance.InanycasewhethertheUnitedStatesreliesonthepublicorprivatesectorescalatinghealthexpendituresfigureintobudgetofgovernmentcorporationsandfamiliestheU.S.healthcaresystem’sfuturemaydependonAmericanswillingnesstodevotemoreoftheirnationalincometohealthcare.Thepassageismostlikelytobe______.
Mostoftheidlerichsufferunspeakableboredoraasthepriceoftheirfreedomfromdrudgery.AttimestheymayfindreliefbyhuntingbiggameinAfricabutthenumberofsuchsensationsislimitedespeciallyafteryouthispast.46.Accordinglymoreintelligentrichmenworknearlyashardasiftheywerepoorwhilerichwomenmostlykeepthemselvesbusywithinnumerabletriflesofwhoseearth-shakingimportancetheyarefirmlypersuaded. 47.Workisdesirableasapreventiveofboredomfortheboredomamanfeelswhendoingnecessarythoughuninterestingworkisasnothingincomparisonwiththeboredomhefeelswhenhavingnothingtodo.Withthisadvantageofworkanotherisassociatednamelythatitmakesholidaysmuchmoredeliciouswhentheycome.48.Providedamandoesnothavetoworksohardastoimpairhisvigorheislikelytofindfarmorezestinfreetimethananidlemancouldpossiblyfind. Thesecondadvantageofmostpaidworkandofsomeunpaidworkisthatitgiveschancesofsuecessandopportunitiesforambition.Inmostworksuccessismeasuredbyincomeandwhileourcapitalisticsocietycontinuesthisisinevitable.Itisonlywherethebestworkisconcernedthatthismeasureceasestobethenaturalonetoapply.49.Thedesirethatmenfeeltoincreasetheirincomeisquiteasmuchadesireforsuccessasfortheextracomfortsthatahigherincomecanprocure.Howeverdullworkmaybeitbecomesbearableifitisameansofbuihliugupareputationwhetherintheworldatlargeoronlyinone’sowncircle.Continuityofpurposeisoneofthemostessentialingredientsofhappinessinthelongrunandformostmenthiscomeschieflythroughtheirwork. 50.Thesatisfactionofkillingtimeandofaffordingsomeoutlethowevermodestforambitionbelongstomostworkandissufficienttomakeevenamanwhoseworkisdullhappierontheaveragethanamanwhohasnoworkatall.Butwhenworkisinterestingitiscapableofgivingsatisfactionofafarhigherorderthanmererelieffromtedium.Thekindsofworkinwhichthereissomeinterestmaybearrangedinahierarchy.Ishallbeginwiththosewhichareonlymildlyinterestingandendwiththosethatareworthytoabsorbthewholeenergiesofagreatman. 46
设常数a>0证明当x>0时不等式e-xx2-ax+1<1成立
设fxy可微且f’i-13=-2f’2-13=1又
已知4元齐次线性方程组的解全是4元方程iix1+x2+x3=0的解求齐次方程组i的解
设常数a与b满足则a+36=______
Allmodernhumanoriginatedinsub-SaharanAfricaaccordingtoanewstudyboastedbyitsfoundersasthe"finalblow"againstanopposingviewpoint.Notsofastsaysoneanthropologistwhofindsflawsintheevidence. ThenewstudypublishedintheJuly19issueofthejournalNaturedeliverswhattheresearcherssaycouldbethefinalverdictinsupportofthesinglepoint"OutofAfrica"theory. Manicaandcolleaguestookmultiplemeasurementsofmorethan4500malefossilskullsfrom105populationsaroundtheglobe.TheycombinedtheresultswithdatafromstudiesofglobalgeneticvariationsinhumansfindingthatbothgeneticandskullvariabilitydecreasedwithdistancefromAfrica.SopopulationsinsoutheasternAfricaheldthehighestvariabilitycomparedwithpopulationsinothercountries. Theresultsheldevenwhenthescientistsaccountedforclimatesinceclimateconditionscanleadtochangesinskullfeatures."Inverycoldclimatesyoutendtogenerateaslightlythickerbrowridge.Whetherornotthat’stokeephorribleblizzardsoutofyoureyesIdon’tknow"Amossaid. Paststudiesbasedonskullmorphologyhavebeenweakandhavesupportedbothofthehumanoriginviews. InhisownresearchHawksisfundingthatnaturalselectionhasledtochangesinthousandsofgenesduringonlythepastfewthousandyears. "I’mreallythinkingjusttheoppositeofthispaper"Hawkssaid."Therearedifferencesintheskullbetweenpopulationsincludingtheirvariabilitybutitismostlyduetoveryrecenteffectsandnottheoriginofmodernhumans." "ThemuhiregionalideaisidenticaltotherecentAfricanoriginideaexceptforitspredictionthatEuropeansandAsianswerepartofthesinglepopulationoforiginanddidn’tbecomeextinct." [A]"HumansseemtohavepouredoutofAfricaspreadoutacrosstheworldbutatareallyquiteuniformratesuchthatyougetthislovelygraduallossofdiversity"saidstudyteammemberWilliamAmosoftheUniversityofCambridge. [B]Allmodernhumansoriginatedfromthesameancestorsandtheykeptevolvingasthesocietyadvances.Somespeciesdiedoutbutothersremainedtoliveontheearthwhichisstillimpossibletosolve. [C]Attheendofthedayaresolutiontothe"OutofAfrica"debatemaybeimpossiblehesaid.Mostoftheevidencecanbeinterpretedassupportingbothhuman-originstheories."It’sreallyhardtofindthetwo"Hawkssaid. [D]Thisstudy"addsastronglineofevidencetotheOutofAfricahypothesisusingsuchmorphology"saidpaleontologistWillHarcourt-SmithoftheAmericanMuseumofNaturalHistoryinNewYork.Harcourt-Smithwasnotinvolvedinthecurrentresearch. [E]DebateovertheoriginsofmodernhumanshassimmeredamonganthropologistsforyearswithonetheoryassertingthatHomosapiensmigratedacrosstheworldfromasinglepointinAfrica.TheothertheorystatesthatmultiplepopulationsofHomosapiensindependentlyevolvedfromHomoerectusinregionsbeyondAfrica. [F]TherecentstudywasfundedbytheBiotechnologyandBiologicalSciencesResearchCouncil.Ithasprovidedconclusiveevidenceconcerningtheactualprocessofhumanevolution. [G]"Wehavecombinedourgeneticdatawithnewmeasurementsofalargesampleofskullstoshowdefinitelythatmodernhumansoriginatedfromasingleareainsub-SaharanAfrica"saidleadresearcherAndreaManicaoftheUniversityofCambridge. 41.______42.______43.______44.______45. 44
由于折旧等因素某机器转售价格Pt是时间t周的减函数其中A是机器的最初价格在任何时间t机器开动就能产生的利润则使转售出去总利润最大时机器使用的时间t=______周ln2≈0.693
设随机变量X服从正态分布Nμσ2σ>0Fx是X的分布函数随机变量Y=FX试求EX+Y
Allmodernhumanoriginatedinsub-SaharanAfricaaccordingtoanewstudyboastedbyitsfoundersasthe"finalblow"againstanopposingviewpoint.Notsofastsaysoneanthropologistwhofindsflawsintheevidence. ThenewstudypublishedintheJuly19issueofthejournalNaturedeliverswhattheresearcherssaycouldbethefinalverdictinsupportofthesinglepoint"OutofAfrica"theory. Manicaandcolleaguestookmultiplemeasurementsofmorethan4500malefossilskullsfrom105populationsaroundtheglobe.TheycombinedtheresultswithdatafromstudiesofglobalgeneticvariationsinhumansfindingthatbothgeneticandskullvariabilitydecreasedwithdistancefromAfrica.SopopulationsinsoutheasternAfricaheldthehighestvariabilitycomparedwithpopulationsinothercountries. Theresultsheldevenwhenthescientistsaccountedforclimatesinceclimateconditionscanleadtochangesinskullfeatures."Inverycoldclimatesyoutendtogenerateaslightlythickerbrowridge.Whetherornotthat’stokeephorribleblizzardsoutofyoureyesIdon’tknow"Amossaid. Paststudiesbasedonskullmorphologyhavebeenweakandhavesupportedbothofthehumanoriginviews. InhisownresearchHawksisfundingthatnaturalselectionhasledtochangesinthousandsofgenesduringonlythepastfewthousandyears. "I’mreallythinkingjusttheoppositeofthispaper"Hawkssaid."Therearedifferencesintheskullbetweenpopulationsincludingtheirvariabilitybutitismostlyduetoveryrecenteffectsandnottheoriginofmodernhumans." "ThemuhiregionalideaisidenticaltotherecentAfricanoriginideaexceptforitspredictionthatEuropeansandAsianswerepartofthesinglepopulationoforiginanddidn’tbecomeextinct." [A]"HumansseemtohavepouredoutofAfricaspreadoutacrosstheworldbutatareallyquiteuniformratesuchthatyougetthislovelygraduallossofdiversity"saidstudyteammemberWilliamAmosoftheUniversityofCambridge. [B]Allmodernhumansoriginatedfromthesameancestorsandtheykeptevolvingasthesocietyadvances.Somespeciesdiedoutbutothersremainedtoliveontheearthwhichisstillimpossibletosolve. [C]Attheendofthedayaresolutiontothe"OutofAfrica"debatemaybeimpossiblehesaid.Mostoftheevidencecanbeinterpretedassupportingbothhuman-originstheories."It’sreallyhardtofindthetwo"Hawkssaid. [D]Thisstudy"addsastronglineofevidencetotheOutofAfricahypothesisusingsuchmorphology"saidpaleontologistWillHarcourt-SmithoftheAmericanMuseumofNaturalHistoryinNewYork.Harcourt-Smithwasnotinvolvedinthecurrentresearch. [E]DebateovertheoriginsofmodernhumanshassimmeredamonganthropologistsforyearswithonetheoryassertingthatHomosapiensmigratedacrosstheworldfromasinglepointinAfrica.TheothertheorystatesthatmultiplepopulationsofHomosapiensindependentlyevolvedfromHomoerectusinregionsbeyondAfrica. [F]TherecentstudywasfundedbytheBiotechnologyandBiologicalSciencesResearchCouncil.Ithasprovidedconclusiveevidenceconcerningtheactualprocessofhumanevolution. [G]"Wehavecombinedourgeneticdatawithnewmeasurementsofalargesampleofskullstoshowdefinitelythatmodernhumansoriginatedfromasingleareainsub-SaharanAfrica"saidleadresearcherAndreaManicaoftheUniversityofCambridge. 41.______42.______43.______44.______45. 42
设f’x在[0+∞上单调减少且证明级数收敛
计算二重积分其中积分区域D是由曲线以及直线x=2围成
设随机变量XY的联合概率密度为讨论随机变量X和Y的相关性和独立性
计算反常积分
设总体X的概率分布为其中参数θ未知且从总体X中抽取一个容量为8的简单随机样本其8个样本值分别是101-11121试求经验分布函数F8x
设且B=P-1AP求矩阵A的特征值与特征向量
PartB Directions: Studythefollowingdrawingcarefullyandwriteanessayabout200wordsinwhichyoushould 1describethedrawingbriefly 2interpretitsintendedmeaningand 3giveyourcomment.
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设总体X的概率分布为其中参数θ未知且从总体X中抽取一个容量为8的简单随机样本其8个样本值分别是101-11121试求θ的矩估计值
已知α1=12-1Tα2=1-32Tα3=411-6T若Aα1=02TAα2=52TAα3=-37T则A=______
设且B=P-1AP求A100
计算累次积分
Mostoftheidlerichsufferunspeakableboredoraasthepriceoftheirfreedomfromdrudgery.AttimestheymayfindreliefbyhuntingbiggameinAfricabutthenumberofsuchsensationsislimitedespeciallyafteryouthispast.46.Accordinglymoreintelligentrichmenworknearlyashardasiftheywerepoorwhilerichwomenmostlykeepthemselvesbusywithinnumerabletriflesofwhoseearth-shakingimportancetheyarefirmlypersuaded. 47.Workisdesirableasapreventiveofboredomfortheboredomamanfeelswhendoingnecessarythoughuninterestingworkisasnothingincomparisonwiththeboredomhefeelswhenhavingnothingtodo.Withthisadvantageofworkanotherisassociatednamelythatitmakesholidaysmuchmoredeliciouswhentheycome.48.Providedamandoesnothavetoworksohardastoimpairhisvigorheislikelytofindfarmorezestinfreetimethananidlemancouldpossiblyfind. Thesecondadvantageofmostpaidworkandofsomeunpaidworkisthatitgiveschancesofsuecessandopportunitiesforambition.Inmostworksuccessismeasuredbyincomeandwhileourcapitalisticsocietycontinuesthisisinevitable.Itisonlywherethebestworkisconcernedthatthismeasureceasestobethenaturalonetoapply.49.Thedesirethatmenfeeltoincreasetheirincomeisquiteasmuchadesireforsuccessasfortheextracomfortsthatahigherincomecanprocure.Howeverdullworkmaybeitbecomesbearableifitisameansofbuihliugupareputationwhetherintheworldatlargeoronlyinone’sowncircle.Continuityofpurposeisoneofthemostessentialingredientsofhappinessinthelongrunandformostmenthiscomeschieflythroughtheirwork. 50.Thesatisfactionofkillingtimeandofaffordingsomeoutlethowevermodestforambitionbelongstomostworkandissufficienttomakeevenamanwhoseworkisdullhappierontheaveragethanamanwhohasnoworkatall.Butwhenworkisinterestingitiscapableofgivingsatisfactionofafarhigherorderthanmererelieffromtedium.Thekindsofworkinwhichthereissomeinterestmaybearrangedinahierarchy.Ishallbeginwiththosewhichareonlymildlyinterestingandendwiththosethatareworthytoabsorbthewholeenergiesofagreatman. 48
设其中fx为连续函数求φ’x
已知A是3阶矩阵αii=123是3维非零列向量若Aαi=iαii=123令α=α1+α2+α3证明αAαA2α线性无关
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