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设(n=1，2，…)，则下列级数中肯定收敛的是______。
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下列命题中哪个是正确的
周期函数f（x）的傅立叶级数收敛于f（x）
若f（x）有任意阶导数，则f（x）的泰勒级数收敛于f（x）
若正项级数
收敛，则
必收敛
正项级数收敛的充分且必要条件是级数的部分和数列有界
设μn≠0n=123且则级数 A发散. B绝对收敛. C条件收敛. D收敛性根据所给条件不能判定.
在下列的论断中错误的是
级数收敛
级数发散
级数改敛,从而收敛
级数收敛
设幂级数anx+1n在x=3处条件收敛则该幂级数的收敛半径R=______．
设n=12则下列级数中肯定收敛的是______
下列命题正确的是
设级数
与级数
都收敛，则
收敛
设级数
收敛，则级数
与级数
都收敛
若正项级数
发散，则
若正项级数
发散，且un≥vn，则级数
收敛
设则下列级数中肯定收敛的是
A
B
C
D
一组n1和一级n2n2＞n1的两组数值变量资料比较用秩和检验有:
n1个秩次1，2，…，n1
n2个秩次1，2，…，n2
n1+ n2个秩次1，2，…，n1+ n2
n2- n1个秩次1，2，…，n2- n1
无限个秩次1，2，…
下列结论正确的是
发散级数加括弧所成的级数仍发散．
若加括弧后的级数收敛，则原级数收敛．
若去括弧后的级数收敛，则原级数收敛。
若去括弧后的级数发散，则原级数发散．
设n=12则下列级数中肯定收敛的是______
设任意项级数a若｜a｜>｜a｜且a=0则对该级数下列哪个结论正确?
必绝对收敛
必发散
必条件收敛
可能收敛，也可能发散
一组n1和一级n2n2＞n1的两组数值变量资料比较用秩和检验有
n1个秩次1，2，…，n1
n2个秩次1，2，…，n2
n1+ n2个秩次1，2，…，n1+ n2
n2- n1个秩次1，2，…，n2- n1
无限个秩次1，2，…
设则下列级数中肯定收敛的是
A
B
C
D
设任意项级数an若｜an｜>｜an+1｜且an=0则对该级数下列哪个结论正确
必条件收敛
必绝对收敛
必发散
可能收敛，也可能发散
下列命题中正确的是
周期函数f（x）的傅立叶级数收敛于f（x）
若f（x）有任意阶导数，则f（x）的泰勒级数收敛于f（x）
若正项级数
收敛，则
必收敛
正项级数收敛的充分且必要条件是级数的部分和数列有界
设幂级数∑anx+1n在x=3处条件收敛则该幂级数的收敛半径R为
-1
4
2
3
设N1﹑N2分别为滚刀﹑工件每分钟转数K﹑Z分别为滚刀﹑工件齿数则滚齿的分齿运动式为
A﹑N1/N2=K/Z
B﹑N1*N2=K*Z
C﹑N2/N1=K/Z
D﹑N1/N2=K*Z
设则下列级数中肯定收敛的是
A
B
C
D
设函数fx在0+∞上具有二阶导数且fx＞0令un=fnn=12则下列结论正确的是______
若u
1
＞u
2
，则u
n
必收敛．
若u
1
＞u
2
，则u
n
必发散．
若u
1
＜u
2
，则u
n
必收敛．
若u
1
＜u
2
，则u
n
必发散．
设有限长序列为xnN1≤n≤N2当N10Z变换的收敛域为
0<
z
<∞
z
>0
z
<∞
z
≤∞
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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.
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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
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______
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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
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=______
由方程所确定的函数z=zxy在点10-1处的全微分dz=______
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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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收敛，则
必收敛 正项级数收敛的充分且必要条件是级数的部分和数列有界
与级数
都收敛，则
收敛 设级数
收敛，则级数
与级数
都收敛 若正项级数
发散，则
若正项级数
发散，且un≥vn，则级数
收敛
收敛，则
必收敛 正项级数收敛的充分且必要条件是级数的部分和数列有界
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