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设A是n阶实对称矩阵，满足A4+2A3+A2+2A=0，若秩r(a)=r，则行列式|A+3E|=______．
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设3阶实对称矩阵A的秩为2λ1=λ2=6是A的二重特征值．若α1=1a0α2=211α3=01-1T
设A是秩为r的n阶实对称矩阵满足A4-3A3+3A2-2A=0．那么矩阵A的n个特征值是______
已知A是四阶实对称矩阵秩rA=3矩阵A满足A4-A3-A2-2A=O则与A相似的对角矩阵是_____
设n阶实对称矩阵A满足A2=E且秩rA+E=k＜n证明B=E+A+A2+A3+A4是正定矩阵并求行列
设n阶实对称矩阵A满足A2=E且秩rA+E=k＜n.Ⅰ求二次型xTAx的规范形Ⅱ证明B=E+A+A2
设A是秩为r的n阶实对称矩阵满足A4-3A3+3A2-2A=0．那么矩阵A的n个特征值是______
设A为m阶实对称矩阵且正定B为m×n阶实矩阵BT为B的转置矩阵试证BTAB为正定矩阵的充分必要条件是
设n阶实对称矩阵A的秩为r且满足A2=A求Ⅰ二次型xTAx的标准形Ⅱ行列式|E+A+A2++An|的
设A是n阶实对称矩阵证明秩rA=n的充分必要条件是存在n阶矩阵B使AB+BTA是正定矩阵．
设A为m阶实对称矩阵且正定B为m×n阶实矩阵BT为B的转置矩阵!试证BTAB为正定矩阵的充分必要条件
设AB均是n阶实对称矩阵则AB是合同矩阵的充分必要条件是矩阵AB
有相同的特征值．
有相同的秩．
有相同的正负惯性指数．
都是可逆矩阵．
设A为m阶实对称矩阵B为m×n实矩阵BT为B的转置矩阵试证BTAB为正定矩阵的充分必要条件是B的秩
设n阶实对称矩阵A满足A2=E且秩rA+E=k＜n求二次型xTAx的规范形
设n阶实对称矩阵A满足A2=E且秩rA+E=k＜n．Ⅰ求二次型xTAx的规范形Ⅱ证明B=E+A+A2
设3阶实对称矩阵A的秩为2λ1=λ2=6是A的二重特征值．若α1=1a0Tα2=211Tα3=01-
已知A是4阶实对称矩阵满足A4-3A2=4E．若秩rA-2E=1．则二次型xTAx的规范形是____
设A是n阶实对称矩阵满足A4+2A3+A2+2A=0若秩rA=r则行列式|A+3E|=______．
设n阶实对称矩阵A的秩为r且满足A2=A求1二次型xTAx的标准形2行列式|E+A+A2++An|的
设AB均n阶实对称矩阵若A与B合同则
A与B有相同的特征值．
A与B有相同的秩．
A与B有相同的特征向量．
A与B有相同的行列式．
设A为m阶实对称矩阵且正定B为m×n阶实矩阵BT为B的转置矩阵试证BTAB为正定矩阵的充分必要条件是
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设f＇x在[01]连续求证级数收敛．
设函数y=yx在-∞+∞有二阶导数且y＇≠0x=xy是y=yx的反函数．Ⅰ试将x=xy所满足的微分方程变换为y=yx所满足的微分方程Ⅱ求变换后的微分方程满足初始条件y＇0=2的解Ⅲ请验证对所求的y=yx在-∞+∞存在反函数．
设fx在包含原点在内的某区间ab内有二阶导数且a＜x＜b证明fx≥xa＜x＜b．
InreadingthepagesofAmericanScientistIhavebeenstruckbythestunningprogressbeingmadeinscienceandengineeringnewphenomenadiscoverednewmaterialssynthesized用合成法合成newmethodsdeveloped.46WhatIseebehindmanyoftheseexcitingstoriesisthewidespreadandevenrevolutionaryuseofdistributedintelligencethatismadepossiblebythewiringofthescientificcommunity.Itismorethanatimesaveroracommunicationenhance;itisenablingustothinkinnewwaysanditsimpactonsocietymaybemonumental.Theterminformationageprobablydoesnotdojusticetothepossibilitiesofthisemergingera.47Thisisanageofknowledgeanddistributedintelligenceinwhichknowledgeisavailabletoanyonelocatedanywhereatanytime;andinwhichpowerinformationandcontrolaremovingfromcentralizedsystemstoindividuals.Thiseracallsforanewformofleadershipandvisionfromtheacademicscienceandengineeringcommunity.Weknowfromcountlessexamplesthattheacademicscienceandtheengineeringhaveenabledoursocietytomakethemostofnewtechnologies.Wewouldn’thavetoday’sadvancedcomputergraphicssystemsifmathematicianshadn’tbeenabletosolveproblemsrelatedtosurfacegeometry.48Wewouldn’thavenetworkscapableofhandlingmassiveamountsofdataifphysicistsandastronomershadn’tcontinuouslyforgedtoolstolookmoredeeplyintosubatomicstructuresandthecosmos.Chemists’effortstosimulatecomplexphenomenaandpredictthepropertiesofmanyelectronsystemshaveinspiredmassivelyparallelarchitecturesforcomputing.Andtheinformationmadeavailablebythesequencingofthehumangenome基因组hascausedustorethinkhowtostoremanipulateandretrievedatamosteffectively.49Itwilltakenewinsightsfromstudiesofhumancognitionlinguisticsneurobiologycomputingandmoretodevelopsystemsthattrulyaugmentourcapacitytolearnandcreate.Thebestmaybeyettocome.DespitebrutallytightconstraintsonfederaldiscretionaryspendingPresidentClintonhassteppedforwardtochampiona3percentincreaseuncorrectedforinflationinthenational1998budget.Thepresident’srequestisonlythefirststepinthecongressionalbudgetprocessahead.50GiventhattheprioritiesofCongresswillalmostcertainlydifferfromthoseofthepresidentitwilltakeanunprecedentedlevelofinputandcommitmentfromtheresearchcommunitytoensuretheinvestmentsinscienceandengineering.
求曲线x2+3xy+y2+1=0在点M02-1处的切线方程与法线方程．
设x∈01证明不等式
InreadingthepagesofAmericanScientistIhavebeenstruckbythestunningprogressbeingmadeinscienceandengineeringnewphenomenadiscoverednewmaterialssynthesized用合成法合成newmethodsdeveloped.46WhatIseebehindmanyoftheseexcitingstoriesisthewidespreadandevenrevolutionaryuseofdistributedintelligencethatismadepossiblebythewiringofthescientificcommunity.Itismorethanatimesaveroracommunicationenhance;itisenablingustothinkinnewwaysanditsimpactonsocietymaybemonumental.Theterminformationageprobablydoesnotdojusticetothepossibilitiesofthisemergingera.47Thisisanageofknowledgeanddistributedintelligenceinwhichknowledgeisavailabletoanyonelocatedanywhereatanytime;andinwhichpowerinformationandcontrolaremovingfromcentralizedsystemstoindividuals.Thiseracallsforanewformofleadershipandvisionfromtheacademicscienceandengineeringcommunity.Weknowfromcountlessexamplesthattheacademicscienceandtheengineeringhaveenabledoursocietytomakethemostofnewtechnologies.Wewouldn’thavetoday’sadvancedcomputergraphicssystemsifmathematicianshadn’tbeenabletosolveproblemsrelatedtosurfacegeometry.48Wewouldn’thavenetworkscapableofhandlingmassiveamountsofdataifphysicistsandastronomershadn’tcontinuouslyforgedtoolstolookmoredeeplyintosubatomicstructuresandthecosmos.Chemists’effortstosimulatecomplexphenomenaandpredictthepropertiesofmanyelectronsystemshaveinspiredmassivelyparallelarchitecturesforcomputing.Andtheinformationmadeavailablebythesequencingofthehumangenome基因组hascausedustorethinkhowtostoremanipulateandretrievedatamosteffectively.49Itwilltakenewinsightsfromstudiesofhumancognitionlinguisticsneurobiologycomputingandmoretodevelopsystemsthattrulyaugmentourcapacitytolearnandcreate.Thebestmaybeyettocome.DespitebrutallytightconstraintsonfederaldiscretionaryspendingPresidentClintonhassteppedforwardtochampiona3percentincreaseuncorrectedforinflationinthenational1998budget.Thepresident’srequestisonlythefirststepinthecongressionalbudgetprocessahead.50GiventhattheprioritiesofCongresswillalmostcertainlydifferfromthoseofthepresidentitwilltakeanunprecedentedlevelofinputandcommitmentfromtheresearchcommunitytoensuretheinvestmentsinscienceandengineering.
已知fx可微且满足方程求fx．
设z=zxy由方程sin2x+sin2y-z=ψx+y+z所确定的函数ψ有连续的二阶导数且ψ＇≠1Ⅰ求dzⅡ记
设a＞0证明不等式
设θ满足.
求连续函数fx使它满足①
设abp为非零常数求．
InreadingthepagesofAmericanScientistIhavebeenstruckbythestunningprogressbeingmadeinscienceandengineeringnewphenomenadiscoverednewmaterialssynthesized用合成法合成newmethodsdeveloped.46WhatIseebehindmanyoftheseexcitingstoriesisthewidespreadandevenrevolutionaryuseofdistributedintelligencethatismadepossiblebythewiringofthescientificcommunity.Itismorethanatimesaveroracommunicationenhance;itisenablingustothinkinnewwaysanditsimpactonsocietymaybemonumental.Theterminformationageprobablydoesnotdojusticetothepossibilitiesofthisemergingera.47Thisisanageofknowledgeanddistributedintelligenceinwhichknowledgeisavailabletoanyonelocatedanywhereatanytime;andinwhichpowerinformationandcontrolaremovingfromcentralizedsystemstoindividuals.Thiseracallsforanewformofleadershipandvisionfromtheacademicscienceandengineeringcommunity.Weknowfromcountlessexamplesthattheacademicscienceandtheengineeringhaveenabledoursocietytomakethemostofnewtechnologies.Wewouldn’thavetoday’sadvancedcomputergraphicssystemsifmathematicianshadn’tbeenabletosolveproblemsrelatedtosurfacegeometry.48Wewouldn’thavenetworkscapableofhandlingmassiveamountsofdataifphysicistsandastronomershadn’tcontinuouslyforgedtoolstolookmoredeeplyintosubatomicstructuresandthecosmos.Chemists’effortstosimulatecomplexphenomenaandpredictthepropertiesofmanyelectronsystemshaveinspiredmassivelyparallelarchitecturesforcomputing.Andtheinformationmadeavailablebythesequencingofthehumangenome基因组hascausedustorethinkhowtostoremanipulateandretrievedatamosteffectively.49Itwilltakenewinsightsfromstudiesofhumancognitionlinguisticsneurobiologycomputingandmoretodevelopsystemsthattrulyaugmentourcapacitytolearnandcreate.Thebestmaybeyettocome.DespitebrutallytightconstraintsonfederaldiscretionaryspendingPresidentClintonhassteppedforwardtochampiona3percentincreaseuncorrectedforinflationinthenational1998budget.Thepresident’srequestisonlythefirststepinthecongressionalbudgetprocessahead.50GiventhattheprioritiesofCongresswillalmostcertainlydifferfromthoseofthepresidentitwilltakeanunprecedentedlevelofinputandcommitmentfromtheresearchcommunitytoensuretheinvestmentsinscienceandengineering.
求累次积分
求其中D由直线x=ax=0y=ay=-a及曲线x2+y2=axa＞0所围．
设求.
设u=uxy由方程组u=fxyztgyzt=0hzt=0确定其中fgh有连续偏导数且g＇zh＇t-g＇th＇z≠0求．
求函数z=x2+12xy+2y2在区域4x2+y2≤．25上的最大值．
设函数fx在闭区间[01]上连续在开区间01内可导且f0=f1=1．求证对任何满足0＜k＜1的常数k存在ξ∈01使f’ξ=-k．
设fx在[02π]上具有一阶连续导数且f＇x≥0证明对于任何正整数n有
某商品的需求函数为Ⅰ求需求Q对价格p的弹性η1和总收益R对价格的弹性12Ⅱ讨论价格p1=2p2=4时当价格上涨1%时需求Q及总收益R是增加还是减少增加或减少的幅度是多少
求数列极限其中．
Directions: Studythefollowingpicturecarefullyandwriteanessayinwhichshould: 1Describethepicturebriefly. 2Interpretitsmeaning. 3Giveyourcommentonit. Youshouldwriteabout160～200wordsneatlyonANSWERSHEET2.
Tourismholidaymakingandtravelarethesedaysmoresignificantsocialphenomenathanmostcommentatorshaveconsidered.Onthefaceofittherecouldnotbeamoretrivialsubjectforabook.Andindeedsincesocialscientistshavehadconsiderabledifficultyexplainingweightiertopicssuchasworkorpoliticsitmightbethoughtthattheywouldhavegreatdifficultiesinaccountingformoretrivialphenomenasuchasholidaymaking.41Howeverthereareinterestingparallelswiththestudyofdeviance.Thisinvolvestheinvestigationofbizarreandidiosyncraticsocialpracticeswhichhappentobedefinedasdeviantinsomesocietiesbutnotnecessarilyinothers.Theassumptionisthattheinvestigationofdeviancecanrevealinterestingandsignificantaspectsofnormalsocieties.Itcouldbesaidthatasimilaranalysiscanbeappliedtotourism.42Tourismisaleisureactivitywhichpresupposesitsoppositenamelyregulatedandorganisedwork.Itisonemanifestationofhowworkandleisureareorganisedasseparateandregulatedspheresofsocialpracticeinmodernsocieties.Indeedactingasatouristisoneofthedefiningcharacteristicsofbeingmodernandthepopularconceptoftourismisthatitisorganizedwithinparticularplacesandoccursforregularisedperiodsoftime.Touristrelationshipsarisefromamovementofpeopletoandtheirstayinvariousdestinations.Thisnecessarilyinvolvessomemovementthatisthejourneyandaperiodofstayinanewplaceorplaces.Thejourneyandthestayarebydefinitionoutsidethenormalplacesofresidenceandworkandareofashort-termandtemporarynatureandthereisaclearintentiontoreturnhomewithinarelativelyshortperiodoftime.43Asubstantialproportionofthepopulationofmodernsocietiesengagesinsuchtouristpractices;newsocialisedformsofprovisionhavedevelopedinordertocopewiththemasscharacterofthegazesoftouristsasopposedtotheindividualcharacteroftravel.Placesarechosentobevisitedandbegazeduponbecausethereisananticipationespeciallythroughdaydreamingandfantasyofintensepleasureseitheronadifferentscaleorinvolvingdifferentsensesfromthosecustomarilyencountered.Suchanticipationisconstructedandsustainedthroughavarietyofnon-touristpracticessuchasfilmsTVliteraturemagazinesrecordsandvideoswhichconstructandreinforcethisdaydreaming.44Touriststendtovisitfeaturesoflandscapeandtownscapewhichseparatethemofffromeverydayexperience.Suchaspectsareviewedbecausetheyaretakentobeinsomesenseoutoftheordinary.Theviewingofthesetouristsightsofteninvolvesdifferentformsofsocialpatterningwithamuchgreatersensitivitytovisualelementsoflandscapeortownscapethanisnormallyfoundineverydaylife.Peoplelingeroverthesesightsinawaythattheywouldnotnormallydointheirhomeenvironmentandthevisionisobjectifiedorcapturedthroughphotographspostcardsfilmsandsoonwhichenablethememorytobeendlesslyreproducedandrecaptured.45Toservicetheburgeoningtouristindustryanarrayofprofessionalshasdevelopedwhoattempttoreproduceever-newobjectsforthetouristtolookat.Theseobjectsorplacesarelocatedinacomplexandchanginghierarchy.Thisdependsupontheinterplaybetweenontheonehandcompetitionbetweeninterestsinvolvedintheprovisionofsuchobjectsandontheotherhandchangingclassgenderandgenerationaldistinctionsoftastewithinthepotentialpopulationofvisitors.Ithasbeensaidthattobeatouristisoneofthecharacteristicsofthemodernexperience.Nottogoawayislikenotpossessingacaroranicehouse.Travelisamarkerofstatusinmodernsocietiesandisalsothoughttobenecessaryforgoodhealth.Theroleoftheprofessionalthereforeistocaterfortheneedsandtastesofthetouristsinaccordancewiththeirclassandoverallexpectations.A.GoodreasonforthestudyoftourismB.DevelopingnewformsofprovisionC.EssenceofmoderntourismD.Tourismvs.leisureE.ExtraordinarinessofmoderntourismF.Exploringroleoftouristprofessionals
Tourismholidaymakingandtravelarethesedaysmoresignificantsocialphenomenathanmostcommentatorshaveconsidered.Onthefaceofittherecouldnotbeamoretrivialsubjectforabook.Andindeedsincesocialscientistshavehadconsiderabledifficultyexplainingweightiertopicssuchasworkorpoliticsitmightbethoughtthattheywouldhavegreatdifficultiesinaccountingformoretrivialphenomenasuchasholidaymaking.41Howeverthereareinterestingparallelswiththestudyofdeviance.Thisinvolvestheinvestigationofbizarreandidiosyncraticsocialpracticeswhichhappentobedefinedasdeviantinsomesocietiesbutnotnecessarilyinothers.Theassumptionisthattheinvestigationofdeviancecanrevealinterestingandsignificantaspectsofnormalsocieties.Itcouldbesaidthatasimilaranalysiscanbeappliedtotourism.42Tourismisaleisureactivitywhichpresupposesitsoppositenamelyregulatedandorganisedwork.Itisonemanifestationofhowworkandleisureareorganisedasseparateandregulatedspheresofsocialpracticeinmodernsocieties.Indeedactingasatouristisoneofthedefiningcharacteristicsofbeingmodernandthepopularconceptoftourismisthatitisorganizedwithinparticularplacesandoccursforregularisedperiodsoftime.Touristrelationshipsarisefromamovementofpeopletoandtheirstayinvariousdestinations.Thisnecessarilyinvolvessomemovementthatisthejourneyandaperiodofstayinanewplaceorplaces.Thejourneyandthestayarebydefinitionoutsidethenormalplacesofresidenceandworkandareofashort-termandtemporarynatureandthereisaclearintentiontoreturnhomewithinarelativelyshortperiodoftime.43Asubstantialproportionofthepopulationofmodernsocietiesengagesinsuchtouristpractices;newsocialisedformsofprovisionhavedevelopedinordertocopewiththemasscharacterofthegazesoftouristsasopposedtotheindividualcharacteroftravel.Placesarechosentobevisitedandbegazeduponbecausethereisananticipationespeciallythroughdaydreamingandfantasyofintensepleasureseitheronadifferentscaleorinvolvingdifferentsensesfromthosecustomarilyencountered.Suchanticipationisconstructedandsustainedthroughavarietyofnon-touristpracticessuchasfilmsTVliteraturemagazinesrecordsandvideoswhichconstructandreinforcethisdaydreaming.44Touriststendtovisitfeaturesoflandscapeandtownscapewhichseparatethemofffromeverydayexperience.Suchaspectsareviewedbecausetheyaretakentobeinsomesenseoutoftheordinary.Theviewingofthesetouristsightsofteninvolvesdifferentformsofsocialpatterningwithamuchgreatersensitivitytovisualelementsoflandscapeortownscapethanisnormallyfoundineverydaylife.Peoplelingeroverthesesightsinawaythattheywouldnotnormallydointheirhomeenvironmentandthevisionisobjectifiedorcapturedthroughphotographspostcardsfilmsandsoonwhichenablethememorytobeendlesslyreproducedandrecaptured.45Toservicetheburgeoningtouristindustryanarrayofprofessionalshasdevelopedwhoattempttoreproduceever-newobjectsforthetouristtolookat.Theseobjectsorplacesarelocatedinacomplexandchanginghierarchy.Thisdependsupontheinterplaybetweenontheonehandcompetitionbetweeninterestsinvolvedintheprovisionofsuchobjectsandontheotherhandchangingclassgenderandgenerationaldistinctionsoftastewithinthepotentialpopulationofvisitors.Ithasbeensaidthattobeatouristisoneofthecharacteristicsofthemodernexperience.Nottogoawayislikenotpossessingacaroranicehouse.Travelisamarkerofstatusinmodernsocietiesandisalsothoughttobenecessaryforgoodhealth.Theroleoftheprofessionalthereforeistocaterfortheneedsandtastesofthetouristsinaccordancewiththeirclassandoverallexpectations.A.GoodreasonforthestudyoftourismB.DevelopingnewformsofprovisionC.EssenceofmoderntourismD.Tourismvs.leisureE.ExtraordinarinessofmoderntourismF.Exploringroleoftouristprofessionals
求下列幂謦数的收敛区间及收敛域
当x→0时都是无穷小量将它们按关于x的阶数从低到高的顺序排列．
设fx在[ab]上连续在ab内可导又b＞a＞0求证存在ξη∈ab使得
设0＜a＜6gx在[aa+b]上连续在aa+b内可导且fa=bfb=afa+b=a+b证明存在一点ξ∈aa+b使得f＇ξ+g＇ξ[fξ-ξ|=1．
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