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dxdx=______
在△ABC中∠ACB=90°AC=BC直线MN经过点C且AD⊥MN于DBE⊥MN于E．1当直线MN绕
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46AnydiscussionoftheAmericaneducationalsystemwouldbelessthancompleteifitdidnotmentiontheemphasisthatmanycollegesanduniversitiesplaceuponthenonacademicsocialextracurricularaspectofeducationoftendefinedaspersonalgrowth.Perhapsausefulwayofviewingthenotionofpersonalgrowthwouldbetopicturetheverylargeandgeneraltermeducationasbeingall-embracingincludingassubsetswithinitacademicandnonacademiccomponents.ThismaybeoneofthemostdifficultconceptstoconveytosomeonewhoisnotintimatelyfamiliarwithAmericanhighereducation.Feweducationalsystemsinothercountriesplacethesameemphasisonthisblendofacademicandpersonaleducation.ThemajorityofcollegesanduniversitiesintheUnitedStatesmakesomeattempttointegratepersonalandintellectualgrowthintheundergraduateyears.47IftheultimategoalofundergraduateeducationinAmericaweresimplytoconveyasetbodyofknowledgethetermofstudiescouldundoubtedlybereduced.Yetthetermsofstudiesareextendedinordertogivestudentsachancetogrowanddevelopinotherways.Numerousopportunitiesaremadeavailabletostudentstobecomeinvolvedinsportsstudentgovernmentmusicalanddramaticorganizationsandcountlessotherorganizedandindividualactivitiesdesignedtoenhanceone’spersonalgrowthandprovidesomerecreationandenjoymentoutsideoftheclassroom.48Experiencewithcampusorganizationsandoff-campuscommunityinvolvementcanbehighlyvaluableinpreparinginternationalstudentsforfutureleadershipintheirprofessionalfieldupontheirreturnhome.ThetypicalAmericancollege’ssupportforextracurricularactivityisperhapsuniqueintheworld.ThisspecialeducationaldimensionbeyondtheclassroomandlaboratoryexperiencedoesnotmeanthatextracurricularparticipationisrequiredtogainanAmericandegree.Itremainsanentirelyoptionalactivitybut49itisnotedherebecauseAmericanshavetraditionallyviewedsuccessinone’sroleasacitizenascloselylinkedtoawell-roundedlifethatincorporatesavarietyofsocialathleticandculturalactivitiesintoaperson’sexperience.AgreatmanyAmericancampusesandcommunitieshaveorganizedspecialextracurricularactivitiesforstudentsfromothercountries.50OnmostcampusesonecanfindaninternationalclubwhichincludesAmericanswherestudentscangettoknowandlearnsociallyfromstudentsfromothercountriesaswellasAmericans.InternationalstudentsarealmostalwaysinvitedthroughorganizedhospitalityactivitiesintothehomesofAmericanslivinginoroutsidetheacademiccommunity.
LongbeforeManlivedontheEarththerewerefishesreptilesbirdsinsectsandsomemammals.Althoughsomeoftheseanimalswereancestorsofkindslivingtodayothersarenowextinctthatistheyhavenodescendantsalivenow.41Veryoccasionallytherocksshowimpressionofskinsothatapartfromcolorwecanbuildupareasonablyaccuratepictureofananimalthatdiedmillionsofyearsago.Thatkindofrockinwhichtheremainsarefoundtellsusmuchaboutthenatureoftheoriginallandoftenoftheplantsthatgrewonitandevenofitsclimate.42Nearlyallofthefossilsthatweknowwerepreservedinrocksformedbywateractionandmostoftheseareofanimalsthatlivedinornearwater.Thusitfollowsthattheremustbemanykindsofmammalsbirdsandinsectsofwhichweknownothing.43Therewerealsocrablikecreatureswhosebodieswerecoveredwithahornysubstance.Thebodysegmentseachhadtwopairsoflegsonepairforwalkingonthesandybottomtheotherforswimming.Theheadwasakindofshieldwithapairofcompoundeyesoftenwiththousandsoflenses.Theywereusuallyaninchortwolongbutsomewere2feet.44Ofthesetheammonitesareveryinterestingandimportant.Theyhaveashellcomposedofmanychamberseachrepresentingatemporaryhomeoftheanimal.Astheyounggrewlargeritgrewanewchamberandsealedoffthepreviousone.ThousandsofthesecanbeseenintherocksontheDorsetCoast.45About75millionyearsagotheAgeofReptileswasoverandmostofthegroupsdiedout.Themammalsquicklydevelopedandwecantracetheevolutionofmanyfamiliaranimalssuchastheelephantandhorse.Manyofthelatermammalsthoughnowextinctwereknowntoprimitivemanandwerefeaturedbyhimincavepaintingsandonbonecarvings.A.Theshellfishhavealonghistoryintherockandmanydifferentkindsareknown.B.Neverthelessweknowagreatdealaboutmanyofthembecausetheirbonesandshellshavebeenpreservedintherocksasfossilsfromthemwecantelltheirsizeandshapehowtheywalkedthekindoffoodtheyate.C.Thefirstanimalswithtruebackboneswerethefishesfirstknownintherocksof375millionyearsago.About300millionyearsagotheamphibianstheanimalsabletolivebothonlandandinwaterappeared.Theyweregiantsometimes8feetlongandmanyofthemlivedintheswampypoolsinwhichourcoalseamorlayerisformed.Theamphibiansgaverisetothereptilesandfornearly150millionyearstheseweretheprincipalformsoflifeonlandintheseaandintheair.D.Thebestindexfossilstendtobemarinecreatures.Theseanimalsevolvedrapidlyandspreadoverlargeoverlargeareasoftheworld.E.Theearliestanimalswhoseremainshavebeenfoundwereallverysimplekindsandlivedinthesea.Laterformsaremorecomplexandamongthesearethesea-liliesrelationsofthestar-fisheswhichhadlongarmsandwereattachedbyalongstalktotheseabedortorocks.F.Whenananimaldiesthebodyitsbonesorshellmayoftenbecarriedawaybystreamsintolakesortheseaandthengetcoveredupbymud.Iftheanimallivedintheseaitsbodywouldprobablysinkandbecoveredwithmud.Moreandmoremudwouldfalluponituntilthebonesorshellbecomeembeddedandpreserved.G.Manyfactorscaninfluencehowfossilsarepreservedinrocks.Remainsofanorganismmaybereplacedbymineralsdissolvedbyanacidicsolutiontoleaveonlytheirimpressionorsimplyreducedtoamorestableform.
LongbeforeManlivedontheEarththerewerefishesreptilesbirdsinsectsandsomemammals.Althoughsomeoftheseanimalswereancestorsofkindslivingtodayothersarenowextinctthatistheyhavenodescendantsalivenow.41Veryoccasionallytherocksshowimpressionofskinsothatapartfromcolorwecanbuildupareasonablyaccuratepictureofananimalthatdiedmillionsofyearsago.Thatkindofrockinwhichtheremainsarefoundtellsusmuchaboutthenatureoftheoriginallandoftenoftheplantsthatgrewonitandevenofitsclimate.42Nearlyallofthefossilsthatweknowwerepreservedinrocksformedbywateractionandmostoftheseareofanimalsthatlivedinornearwater.Thusitfollowsthattheremustbemanykindsofmammalsbirdsandinsectsofwhichweknownothing.43Therewerealsocrablikecreatureswhosebodieswerecoveredwithahornysubstance.Thebodysegmentseachhadtwopairsoflegsonepairforwalkingonthesandybottomtheotherforswimming.Theheadwasakindofshieldwithapairofcompoundeyesoftenwiththousandsoflenses.Theywereusuallyaninchortwolongbutsomewere2feet.44Ofthesetheammonitesareveryinterestingandimportant.Theyhaveashellcomposedofmanychamberseachrepresentingatemporaryhomeoftheanimal.Astheyounggrewlargeritgrewanewchamberandsealedoffthepreviousone.ThousandsofthesecanbeseenintherocksontheDorsetCoast.45About75millionyearsagotheAgeofReptileswasoverandmostofthegroupsdiedout.Themammalsquicklydevelopedandwecantracetheevolutionofmanyfamiliaranimalssuchastheelephantandhorse.Manyofthelatermammalsthoughnowextinctwereknowntoprimitivemanandwerefeaturedbyhimincavepaintingsandonbonecarvings.A.Theshellfishhavealonghistoryintherockandmanydifferentkindsareknown.B.Neverthelessweknowagreatdealaboutmanyofthembecausetheirbonesandshellshavebeenpreservedintherocksasfossilsfromthemwecantelltheirsizeandshapehowtheywalkedthekindoffoodtheyate.C.Thefirstanimalswithtruebackboneswerethefishesfirstknownintherocksof375millionyearsago.About300millionyearsagotheamphibianstheanimalsabletolivebothonlandandinwaterappeared.Theyweregiantsometimes8feetlongandmanyofthemlivedintheswampypoolsinwhichourcoalseamorlayerisformed.Theamphibiansgaverisetothereptilesandfornearly150millionyearstheseweretheprincipalformsoflifeonlandintheseaandintheair.D.Thebestindexfossilstendtobemarinecreatures.Theseanimalsevolvedrapidlyandspreadoverlargeoverlargeareasoftheworld.E.Theearliestanimalswhoseremainshavebeenfoundwereallverysimplekindsandlivedinthesea.Laterformsaremorecomplexandamongthesearethesea-liliesrelationsofthestar-fisheswhichhadlongarmsandwereattachedbyalongstalktotheseabedortorocks.F.Whenananimaldiesthebodyitsbonesorshellmayoftenbecarriedawaybystreamsintolakesortheseaandthengetcoveredupbymud.Iftheanimallivedintheseaitsbodywouldprobablysinkandbecoveredwithmud.Moreandmoremudwouldfalluponituntilthebonesorshellbecomeembeddedandpreserved.G.Manyfactorscaninfluencehowfossilsarepreservedinrocks.Remainsofanorganismmaybereplacedbymineralsdissolvedbyanacidicsolutiontoleaveonlytheirimpressionorsimplyreducedtoamorestableform.
设二维随机变量XY在区域D://0＜x＜1|y|=x内服从均均分布求关于X的边缘概率密度函数及随机变量Z=2X+1的方差DZ
设A=ijn×n是正交矩阵将A以行分块为A=α1α2αnT则方程组AX=bb=b1bnT的通解为______
设总体X服从于正态分布Nμσ2σ＞0从该总体中抽取简单随机样本X1X2X2nn≥2其样本均值为求统计量Y=的数学期望EY
如果
已知随机变量X和Y相互独立则X～N11Y～N14又PaX+bY≤0=则a与b应满足关系式______
设随机变量X与Y服从正态分布X～Nμ42Y～Nμ52记P1=Px≤μ-4P2=Y≥μ+5则______
已知函数fx具有任意阶导数且f’x=[fx]2则当n为大于2的正整数时fx的n阶导数fnx为______
设fx在-∞+∞内是可导的奇函数则下列函数中是奇函数的是______
Donotsignyourownnameattheendoftheletter.Use"DepartmentofChineseLanguageandLiterature"instead. Donotwritetheaddress.
求微分方程Y+5y’+6y=2e-x的通解
A是n阶矩阵且A3=0则______
设A是n阶正定矩阵E是n阶单位阵证明A+E的行列式大于1
设A为n阶方阵A*为A的伴随矩阵且A11≠0证明方程组Ax=bb≠0有无穷多解的充要条件中b为A*X=0的解
设X服从正态分布N022而X1X2X15为来自总体X的简单随机样本则随机变量所服从的分布为______
=______
由方程所确定的函数z=zxy在点10-1处的全微分dz=______
LongbeforeManlivedontheEarththerewerefishesreptilesbirdsinsectsandsomemammals.Althoughsomeoftheseanimalswereancestorsofkindslivingtodayothersarenowextinctthatistheyhavenodescendantsalivenow.41Veryoccasionallytherocksshowimpressionofskinsothatapartfromcolorwecanbuildupareasonablyaccuratepictureofananimalthatdiedmillionsofyearsago.Thatkindofrockinwhichtheremainsarefoundtellsusmuchaboutthenatureoftheoriginallandoftenoftheplantsthatgrewonitandevenofitsclimate.42Nearlyallofthefossilsthatweknowwerepreservedinrocksformedbywateractionandmostoftheseareofanimalsthatlivedinornearwater.Thusitfollowsthattheremustbemanykindsofmammalsbirdsandinsectsofwhichweknownothing.43Therewerealsocrablikecreatureswhosebodieswerecoveredwithahornysubstance.Thebodysegmentseachhadtwopairsoflegsonepairforwalkingonthesandybottomtheotherforswimming.Theheadwasakindofshieldwithapairofcompoundeyesoftenwiththousandsoflenses.Theywereusuallyaninchortwolongbutsomewere2feet.44Ofthesetheammonitesareveryinterestingandimportant.Theyhaveashellcomposedofmanychamberseachrepresentingatemporaryhomeoftheanimal.Astheyounggrewlargeritgrewanewchamberandsealedoffthepreviousone.ThousandsofthesecanbeseenintherocksontheDorsetCoast.45About75millionyearsagotheAgeofReptileswasoverandmostofthegroupsdiedout.Themammalsquicklydevelopedandwecantracetheevolutionofmanyfamiliaranimalssuchastheelephantandhorse.Manyofthelatermammalsthoughnowextinctwereknowntoprimitivemanandwerefeaturedbyhimincavepaintingsandonbonecarvings.A.Theshellfishhavealonghistoryintherockandmanydifferentkindsareknown.B.Neverthelessweknowagreatdealaboutmanyofthembecausetheirbonesandshellshavebeenpreservedintherocksasfossilsfromthemwecantelltheirsizeandshapehowtheywalkedthekindoffoodtheyate.C.Thefirstanimalswithtruebackboneswerethefishesfirstknownintherocksof375millionyearsago.About300millionyearsagotheamphibianstheanimalsabletolivebothonlandandinwaterappeared.Theyweregiantsometimes8feetlongandmanyofthemlivedintheswampypoolsinwhichourcoalseamorlayerisformed.Theamphibiansgaverisetothereptilesandfornearly150millionyearstheseweretheprincipalformsoflifeonlandintheseaandintheair.D.Thebestindexfossilstendtobemarinecreatures.Theseanimalsevolvedrapidlyandspreadoverlargeoverlargeareasoftheworld.E.Theearliestanimalswhoseremainshavebeenfoundwereallverysimplekindsandlivedinthesea.Laterformsaremorecomplexandamongthesearethesea-liliesrelationsofthestar-fisheswhichhadlongarmsandwereattachedbyalongstalktotheseabedortorocks.F.Whenananimaldiesthebodyitsbonesorshellmayoftenbecarriedawaybystreamsintolakesortheseaandthengetcoveredupbymud.Iftheanimallivedintheseaitsbodywouldprobablysinkandbecoveredwithmud.Moreandmoremudwouldfalluponituntilthebonesorshellbecomeembeddedandpreserved.G.Manyfactorscaninfluencehowfossilsarepreservedinrocks.Remainsofanorganismmaybereplacedbymineralsdissolvedbyanacidicsolutiontoleaveonlytheirimpressionorsimplyreducedtoamorestableform.
若=+∞则级数______
设ab为正常系数λ为非负常数微分方程Ⅰ求该方程的通解Ⅱ证明当λ=0时当λ＞0时
设z=f2x-yysinx其中fuv具有连续的二阶偏导数求
______.
幂级数的和函数为______
假设生产和销售某产品的收益R是产量的q二次函数经统计得知当产量q分别为024时总收入R分别为068万元试确定R与q之间的函数关系
设λ1λ2是n阶矩阵A的特征值α1α2分别是A的属于λ1λ2的特征向量则______
46AnydiscussionoftheAmericaneducationalsystemwouldbelessthancompleteifitdidnotmentiontheemphasisthatmanycollegesanduniversitiesplaceuponthenonacademicsocialextracurricularaspectofeducationoftendefinedaspersonalgrowth.Perhapsausefulwayofviewingthenotionofpersonalgrowthwouldbetopicturetheverylargeandgeneraltermeducationasbeingall-embracingincludingassubsetswithinitacademicandnonacademiccomponents.ThismaybeoneofthemostdifficultconceptstoconveytosomeonewhoisnotintimatelyfamiliarwithAmericanhighereducation.Feweducationalsystemsinothercountriesplacethesameemphasisonthisblendofacademicandpersonaleducation.ThemajorityofcollegesanduniversitiesintheUnitedStatesmakesomeattempttointegratepersonalandintellectualgrowthintheundergraduateyears.47IftheultimategoalofundergraduateeducationinAmericaweresimplytoconveyasetbodyofknowledgethetermofstudiescouldundoubtedlybereduced.Yetthetermsofstudiesareextendedinordertogivestudentsachancetogrowanddevelopinotherways.Numerousopportunitiesaremadeavailabletostudentstobecomeinvolvedinsportsstudentgovernmentmusicalanddramaticorganizationsandcountlessotherorganizedandindividualactivitiesdesignedtoenhanceone’spersonalgrowthandprovidesomerecreationandenjoymentoutsideoftheclassroom.48Experiencewithcampusorganizationsandoff-campuscommunityinvolvementcanbehighlyvaluableinpreparinginternationalstudentsforfutureleadershipintheirprofessionalfieldupontheirreturnhome.ThetypicalAmericancollege’ssupportforextracurricularactivityisperhapsuniqueintheworld.ThisspecialeducationaldimensionbeyondtheclassroomandlaboratoryexperiencedoesnotmeanthatextracurricularparticipationisrequiredtogainanAmericandegree.Itremainsanentirelyoptionalactivitybut49itisnotedherebecauseAmericanshavetraditionallyviewedsuccessinone’sroleasacitizenascloselylinkedtoawell-roundedlifethatincorporatesavarietyofsocialathleticandculturalactivitiesintoaperson’sexperience.AgreatmanyAmericancampusesandcommunitieshaveorganizedspecialextracurricularactivitiesforstudentsfromothercountries.50OnmostcampusesonecanfindaninternationalclubwhichincludesAmericanswherestudentscangettoknowandlearnsociallyfromstudentsfromothercountriesaswellasAmericans.InternationalstudentsarealmostalwaysinvitedthroughorganizedhospitalityactivitiesintothehomesofAmericanslivinginoroutsidetheacademiccommunity.
当x→0时fx=x-sinax与gx=x2ln1-bx是等价无穷小则______
若函数y=fx有f’x0=则当Δx→0时该函数在x=x0点外的微分dy是______
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