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判断下列反常积分的敛散性,如果是收敛的求出反常积分值.
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函数fx在[1+∞上连续且反常积分[*]收敛并满足[*]则函数fx的表达式是______.
函数fx在[1+∞上连续且反常积分收敛并满足 则函数fx的表达式是______.
判断下列反常积分的敛散性如果是收敛的要求出反常积分的值.
判断下列反常积分的敛散性如果是收敛的求出反常积分值.[*]
反常积分
收敛于0
收敛于
ln3
收敛于
ln2
发散
已知k>0对于反常积分的敛散情况下面判断正确的是______
当k>1时,积分发散.
当k≤1时,积分发散.
敛散性与k无关,必收敛.
敛散性与k无关,必发散.
设函数fx在[1+∞上连续且反常积分[*]收敛并满足[*][*]则函数fx的表达式是______.
设
(A) 为反常积分,且发散.
(B) 为反常积分,且收敛.
(C) 不是反常积分,且其值为10.
(D) 不是反常积分,且其值为.
设mn均是正整数则反常积分的收敛性
仅与m的取值有关.
仅与n的取值有关.
与m,n的取值都有关.
与m,n的取值都无关.
判断下列反常积分的敛散性如果是收敛的要求出反常积分的值.
下列反常积分① 中收敛的是
①②
①③
②④
③④
设mn是正整数则反常积分的收敛性
仅与m的取值有关
仅与n有关
与m,n取值有关
与m,n取值都无关
设常数a∈-∞+∞讨论反常积分的敛散性.又当上述反常积分收敛时记确定当a取何值时Ia取得最小值.
计算下列反常积分广义积分的值.[*]
下列反常积分发散的是.
A
B
C
D
设a>0p为常数则反常积分
收敛(对任何p)
发散(对任何p)
当p≤1时收敛,当p>1时发散
当p≤1时发散,当p>1时收敛
下列关于反常积分的命题①设fx是-∞+∞上的连续奇函数则②设fx在-∞+∞上连续且存在则必收敛且③若
(A) 1个.
(B) 2个.
(C) 3个.
(D) 4个.
反常积分
收敛于π
收敛于π/2
收敛于π/4
发散
设常数a∈-∞+∞讨论反常积分的敛散性.又当上述反常积分收敛时记确定当a取何值时Ia取得最小值.
设ab为常数则反常积分
收敛(对任何q)
发散(对任何q)
当q<1时收敛,当q≥1时发散
当q<1时发散,当q≥1时收敛
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WhataccountsforthegreatoutburstofmajorinventionsinearlyAmerica―breakthroughssuchasthetelegraphthesteamboatandtheweavingmachine AmongthemanyshapingfactorsIwouldsingleoutthecountry’’sexcellentelementaryschools;alaborforcethatwelcomedthenewtechnology;thepracticeofgivingpremiumstoinventors;andabovealltheAmericangeniusfornonverbalspatialthinkingaboutthingstechnological. WhymentiontheelementaryschoolsBecausethankstotheseschoolsourearlymechanicespeciallyintheNewEnglandandMiddleAtlanticstatesweregenerallyliterateandathomeinarithmeticandinsomeaspectsofgeometryandtrigonometry. AcuteforeignobserversrelatedAmericanadaptivenessandinventivenesstothiseducationaladvantage.AsamemberofaBritishcommissionvisitingherein1853reportedWithamindpreparedbythoroughschooldisciplinetheAmericanboydevelopsrapidlyintotheskilledworkman. Afurtherstimulustoinventioncamefromthepremiumsystemwhichprecededourpatentsystemandforyearsranparallelwithit.Thisapproachoriginatedabroadofferedinventorsmedalscashprizesandotherincentives. IntheUnitedStatesmultitudesofpremiumsfornewdeviceswereawardedatcountryfairsandattheindustrialfairsinmajorcities.Americansflockedtothesefairstoadmirethenewmachinesandthustorenewtheirfaithinthebeneficenceoftechnologicaladvance. GiventhisoptimisticapproachtotechnologicalinnovationtheAmericanworkertookreadilytothatspecialkindofnonverbalthinkingrequiredinmechanicaltechnology.AsEugeneFergusonhaspointedoutAtechnologistthinksaboutobjectsthatcannotbereducedtounambiguousverbaldescriptions;theyaredealtwithinhismindbyavisualnonverbalprocess...Thedesignerandtheinventor...areabletoassembleandmanipulateintheirmindsdevicesthatasyetdonotexist. Thisnonverbalspatialthinkingcanbejustascreativeaspaintingandwriting.RobertFultononcewroteThemechanicshouldsitdownamongleversscrewswedgeswheelsetc.likeapoetamongthelettersofthealphabetconsideringthemasanexhibitionofhisthoughtsinwhichanewarrangementtransmitsanewidea. Whenalltheseshapingforces―schoolsopenattitudesthepremiumsystemageniusforspatialthinking―interactedwithoneanotherontherichU.S.mainlandtheyproducedthatAmericancharacteristicemulation.Todaythatwordimpliesmereimitation.Butinearliertimesitmeantafriendlybutcompetitivestrivingforfameandexcellence. AccordingtotheauthorthegreatoutburstofmajorinventionsinearlyAmericawasinalargepartdueto_________________.
设Fx是函数fx在区间I上的原函数则
下列计算
设fex=x则函数fx在区间[12]上的平均值等于
若的原函数Fx的表达式中Ⅰ不包含对数函数Ⅱ不含反正切函数则其中的常数a和b分别满足条件______.
Inlessthan30years’’timetheStarTrekholodeckwillbeareality.Directlinksbetweenthebrain’’snervoussystemandacomputerwillalsocreatefullsensoryvirtualenvironmentsallowingvirtualvacationslikethoseinthefilmTotalRecall. 71.Therewillbetelevisionchatshowshostedbyrobotsandcarswithpollutionmonitorsthatwilldisablethemwhentheyoffend.72.Childrenwillplaywithdollsequippedwithpersonalitychipscomputerswithin-builtpersonalitieswillberegardedasworkmatesratherthantoolsrelaxationwillbeinfrontofsmell-televisionanddigitalagewillhavearrived. AccordingtoBT’’sfuturologistIanPearsontheseareamongthedevelopmentsscheduledforthefirstfewdecadesofthenewmillenniumaperiodof1000yearswhensupercomputerswilldramaticallyaccelerateprogressinallareasoflife. 73.Pearsonhaspiecedtogethertheworkofhundredsofresearchersaroundtheworldtoproduceauniquemillenniumtechnologycalendarthatgivesthelatestdateswhenwecanexpecthundredsorkeybreakthroughsanddiscoveriestotakeplace.Someofthebiggestdevelopmentswillbeinmedicineincludinganextendedlifeexpectancyanddozensofartificialorganscomingintousebetweennowand2040. Pearsonalsopredictsabreakthroughincomputer-humanlinks.BylinkingdirectlytoournervoussystemcomputerscouldpickupwhatwefeelandhopefullysimulatefeelingtoosothatwecanstarttodevelopfullsensoryenvironmentsratherliketheholidaysinTotalRecallortheStarTrekholodeckhesays.74.ButthatPearsonpointsoutisonlythestartofman-machineintegration:Itwillbethebeginningofthelongprocessofintegrationthatwillultimatelyleadtoafullyelectronichumanbeforetheendofthenextcentury. ThroughhisresearchPearsonisabletoputdatestomostofthebreakthroughsthatcanbepredicted.Howevertherearestillnoforecastsforwhenfaster-that-lighttravelwillbeavailableorwhenhumancloningwillbeperfectedorwhentimetravelwillbepossible.Buthedoesexpectsocialproblemsasaresultoftechnologicaladvances.Aboominneighborhoodsurveillancecameraswillforexamplecauseproblemsin2010whilethearrivalofsyntheticlifelikerobotswillmeanpeoplemaynotbeabletodistinguishbetweentheirhumanfriendsandthedroids.75.Andhomeapplianceswillalsobecomesosmartthatcontrollingandoperatingthemwillresultinthebreakoutofanewpsychologicaldisorder--kitchenrage.
Scienceinpracticedependsfarlessontheexperimentsitpreparesthanonthepreparednessofthemindsofthemenwhowatchtheexperiments.SirIsaacNewtonsupposedlydiscoveredgravitythroughthefallofanapple.Appleshadbeenfallinginmanyplacesforcenturiesandthousandsofpeoplehadseenthemfall.ButNewtonforyearshadbeencuriousaboutthecauseoftheorbitalmotionofthemoonandplanets.WhatkepttheminplaceWhydidn’’ttheyfalloutoftheskyThefactthattheapplefelldowntowardtheearthandnotupintothetreeansweredthequestionhehadbeenaskinghimselfaboutthoselargerfruitsoftheheavensthemoonandtheplanets. HowmanymenwouldhaveconsideredthepossibilityofanapplefallingupintothetreeNewtondidbecausehewasnottryingtopredictanything.Hewasjustwondering.Hismindwasreadyfortheunpredictable.Unpredictabilityispartoftheessentialnatureofresearch.Ifyoudon’’thaveunpredictablethingsyoudon’’thaveresearch.Scientiststendtoforgetthiswhenwritingtheircutanddriedreportsforthetechnicaljournalsbuthistoryisfilledwithexamplesofit. Intalkingtosomescientistsparticularlyyoungeronesyoumightgathertheimpressionthattheyfindthescientificmethodasubstituteforimaginativethought.I’’veattendedresearchconferenceswhereascientisthasbeenaskedwhathethinksabouttheadvisabilityofcontinuingacertainexperiment.Thescientisthasfrownedlookedatthegraphsandsaidthedataarestillinconclusive.WeknowthatthemenfromthebudgetofficehavesaidbutwhatdoyouthinkIsitworthwhilegoingonWhatdoyouthinkwemightexpectThescientisthasbeenshockedathavingevenbeenaskedtospeculate. Whatthisamountstoofcourseisthatthescientisthasbecomethevictimofhisownwritings.Hehasputforwardunquestionedclaimssoconsistentlythathenotonlybelievesthemhimselfbuthasconvincedindustrialandbusinessmanagementthattheyaretrue.Ifexperimentsareplannedandcarriedoutaccordingtoplanasfaithfullyasthereportsinthesciencejournalsindicatethenitisperfectlylogicalformanagementtoexpectresearchtoproduceresultsmeasurableindollarsandcents.Itisentirelyreasonableforauditorstobelievethatscientistswhoknowexactlywheretheyaregoingandhowtheywillgetthereshouldnotbedistractedbythenecessityofkeepingoneeyeonthecashregisterwhiletheothereyeisonthemicroscope.Norifregularityandconformitytoastandardpatternareasdesirabletothescientistasthewritingofhispaperswouldappeartoreflectismanagementtobeblamedfordiscriminatingagainsttheoddballsamongresearchersinfavorofmoreconventionalthinkerswhoworkwellwiththeteam. Itseemsthatsomeyoungscientists_______________.
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It’’safunnythinghappiness.Peoplerefertoitassomethingtheywantsomethingmissingasifitcouldbesecurediftheyonlyknewwheretofindit.Lackofitisblamedonpastrelationshipsandhopeforitplacedonfuturelovers.Desireforitbecomesarestlessquest.Yetoverandagainintherapyitisclearthatahungrypursuitfortheillusivestateofhappinessonlyendsinfrustrationandyetmoreunhappiness. WhenIaskamanwho’’sjustturned40andwantstotrypsychotherapytotellmeaboutthedisappointmentshementionshereelsoffalist:aloveaffairthatlostitszest;aworkprojectruinedbyacolleague;aholidayspoiledbytheweather;aplanhaltedbyillhealth.Allwerepotentialroutestohappiness.Anditisthisendlessfeelingofthingsbeingspoiltthatmakeshimfeelletdownbylifeandunhappy. Hetellsmethathehadbeenawillfulchild.Hewashesaysspoiltrottenbyverylovingparents.Theyhadsufferedmuchhardshipintheirownlivesandwhenhardworkandgoodluckmadethemwellofftheydecidedthathetheironlysonwouldhavealltheyhadlackedandmore. Hehadwantedfornothing.Yetthiscamewithacost.Forhavingeverythingonaplatebeforehehadevendevelopedanappetitehadrobbedhimofthechancetoreachandstruggleforsomethingmeaningfulandofhisveryown.Therehadneverbeenanemptyspacehehadenjoyedworkingtofill.Littlewonderhewasunabletoremainattachedtoanythingoranyoneafterfrustrationsetin.Workingthroughdifficultysimplyhadn’’teverbeenaskedofhim. Whilehopefullyaby-productofdevelopingemotionalmaturityhappinesswasnotItoldhimaspecifictherapeuticaim.Buttherapycouldofferthechallengetostaywithandsograduallyunderstandthemeaningofhisunhappinessratherthanboltingwhenthegoinggotrough.Thenotionthatwecanuncoverameaningwithinoursufferingsupportsthewholetherapeuticventure.Byworkingtowardsunderstandingthereasonsforhisdisappointmentsthismanhadthechancetobeginreshapinghisownlifejourney.Thiswasunlikelytogivehimhappinessasagivenconstantbutcouldenablehimtodevelopsomethingfarmoreimportant.AsC.G.JungthefounderofAnalyticalPsychologysaid:Theprincipalaimofpsychotherapyisnottotransportthepatienttoanimpossiblestateofhappinessbuttohelphimacquiresteadfastnessandphilosophicpatienceinthefaceofsuffering.Lifedemandsforitscompletionandfulfillmentabalancebetweenjoyandsorrow. Thepatient’’sunhappinessresultsprimarilyfromhis
设x≠0则∫fxdx______.
WhataccountsforthegreatoutburstofmajorinventionsinearlyAmerica―breakthroughssuchasthetelegraphthesteamboatandtheweavingmachine AmongthemanyshapingfactorsIwouldsingleoutthecountry’’sexcellentelementaryschools;alaborforcethatwelcomedthenewtechnology;thepracticeofgivingpremiumstoinventors;andabovealltheAmericangeniusfornonverbalspatialthinkingaboutthingstechnological. WhymentiontheelementaryschoolsBecausethankstotheseschoolsourearlymechanicespeciallyintheNewEnglandandMiddleAtlanticstatesweregenerallyliterateandathomeinarithmeticandinsomeaspectsofgeometryandtrigonometry. AcuteforeignobserversrelatedAmericanadaptivenessandinventivenesstothiseducationaladvantage.AsamemberofaBritishcommissionvisitingherein1853reportedWithamindpreparedbythoroughschooldisciplinetheAmericanboydevelopsrapidlyintotheskilledworkman. Afurtherstimulustoinventioncamefromthepremiumsystemwhichprecededourpatentsystemandforyearsranparallelwithit.Thisapproachoriginatedabroadofferedinventorsmedalscashprizesandotherincentives. IntheUnitedStatesmultitudesofpremiumsfornewdeviceswereawardedatcountryfairsandattheindustrialfairsinmajorcities.Americansflockedtothesefairstoadmirethenewmachinesandthustorenewtheirfaithinthebeneficenceoftechnologicaladvance. GiventhisoptimisticapproachtotechnologicalinnovationtheAmericanworkertookreadilytothatspecialkindofnonverbalthinkingrequiredinmechanicaltechnology.AsEugeneFergusonhaspointedoutAtechnologistthinksaboutobjectsthatcannotbereducedtounambiguousverbaldescriptions;theyaredealtwithinhismindbyavisualnonverbalprocess...Thedesignerandtheinventor...areabletoassembleandmanipulateintheirmindsdevicesthatasyetdonotexist. Thisnonverbalspatialthinkingcanbejustascreativeaspaintingandwriting.RobertFultononcewroteThemechanicshouldsitdownamongleversscrewswedgeswheelsetc.likeapoetamongthelettersofthealphabetconsideringthemasanexhibitionofhisthoughtsinwhichanewarrangementtransmitsanewidea. Whenalltheseshapingforces―schoolsopenattitudesthepremiumsystemageniusforspatialthinking―interactedwithoneanotherontherichU.S.mainlandtheyproducedthatAmericancharacteristicemulation.Todaythatwordimpliesmereimitation.Butinearliertimesitmeantafriendlybutcompetitivestrivingforfameandexcellence. Atechnologistcanbecomparedtoanartistbecause_________________.
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MoneyspentonadvertisingismoneyspentaswellasanyIknowof.Itservesdirectlytoassistarapiddistributionofgoodsatreasonablepricestherebyestablishingafirmhomemarketandsomakingitpossibletoprovideforexportatcompetitiveprices.Bydrawingattentiontonewideasithelpsenormouslytoraisestandardsofliving.Byhelpingtoincreasedemanditensuresanincreasedneedforlabourandisthereforeaneffectivewaytofightunemployment.Itlowersthecostsofmanyservices:withoutadvertisementsyourdailynewspaperwouldcostfourtimesasmuchthepriceofyourtelevisionlicencewouldneedtobedoubledandtravelbybusortubewouldcost20percentmore. Andperhapsmostimportantofalladvertisingprovidesaguaranteeofreasonablevalueintheproductsandservicesyoubuy.Apartfromthefactthattwenty-sevenActsofParliamentgovernthetermsofadvertisingnoregularadvertiserdarepromoteaproductthatfailstoliveuptothepromiseofhisadvertisements.Hemightfoolsomepeopleforalittlewhilethroughmisleadingadvertising.Hewillnotdosoforlongformercifullythepublichasthegoodsensenottobuytheinferiorarticlemorethanonce.IfyouseeanarticleconsistentlyadvertiseditisthesurestproofIknowthatthearticledoeswhatisclaimedforitandthatitrepresentsgoodvalue. AdvertisingdoesmoreforthematerialbenefitofthecommunitythananyotherforceIcanthinkof. ThereisonepointIfeelIoughttotouchon.RecentlyIheardawell-knowntelevisionpersonalitydeclarethathewasagainstadvertisingbecauseitpersuadesratherthaninforms.Hewasdrawingexcessivelyfinedistinctions.Ofcourseadvertisingseekstopersuade. Ifitsmessagewereconfinedmerelytoinformation―andthatinitselfwouldbedifficultifnotimpossibletoachieveforevenadetailsuchasthechoiceofthecolourofashirtissubtletypersuasiveadvertisingwouldbesoboringthatnoonewouldpayanyattention.Butperhapsthatiswhatthewell-knowntelevisionpersonalitywants. Theauthordeemsthatthewell-knownTVpersonalityis_______________.
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下列结论不正确的是
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设Fx是函数fx=max{xx2}的一个原函数.则
下列结论正确的是
下列等式或结论正确的是
下列命题①设∫fxdx=Fx+C则对任意函数gx有∫f[gx]dx=F[gx]+C ②设函数fx在某区间上连续可导且f’x≠0.又f-1x是其反函数且∫fxdx=Fx+C则 ∫f-1xdx=xf-1x-F[f-1x]+C ③设∫fxdx=Fx+Cx∈-∞+∞常数a≠0则∫faxdx=Fax+C. ④设∫fxdx=Fx+Cx∈-∞+∞则 中正确的是
下列命题不正确的是
It’’safunnythinghappiness.Peoplerefertoitassomethingtheywantsomethingmissingasifitcouldbesecurediftheyonlyknewwheretofindit.Lackofitisblamedonpastrelationshipsandhopeforitplacedonfuturelovers.Desireforitbecomesarestlessquest.Yetoverandagainintherapyitisclearthatahungrypursuitfortheillusivestateofhappinessonlyendsinfrustrationandyetmoreunhappiness. WhenIaskamanwho’’sjustturned40andwantstotrypsychotherapytotellmeaboutthedisappointmentshementionshereelsoffalist:aloveaffairthatlostitszest;aworkprojectruinedbyacolleague;aholidayspoiledbytheweather;aplanhaltedbyillhealth.Allwerepotentialroutestohappiness.Anditisthisendlessfeelingofthingsbeingspoiltthatmakeshimfeelletdownbylifeandunhappy. Hetellsmethathehadbeenawillfulchild.Hewashesaysspoiltrottenbyverylovingparents.Theyhadsufferedmuchhardshipintheirownlivesandwhenhardworkandgoodluckmadethemwellofftheydecidedthathetheironlysonwouldhavealltheyhadlackedandmore. Hehadwantedfornothing.Yetthiscamewithacost.Forhavingeverythingonaplatebeforehehadevendevelopedanappetitehadrobbedhimofthechancetoreachandstruggleforsomethingmeaningfulandofhisveryown.Therehadneverbeenanemptyspacehehadenjoyedworkingtofill.Littlewonderhewasunabletoremainattachedtoanythingoranyoneafterfrustrationsetin.Workingthroughdifficultysimplyhadn’’teverbeenaskedofhim. Whilehopefullyaby-productofdevelopingemotionalmaturityhappinesswasnotItoldhimaspecifictherapeuticaim.Buttherapycouldofferthechallengetostaywithandsograduallyunderstandthemeaningofhisunhappinessratherthanboltingwhenthegoinggotrough.Thenotionthatwecanuncoverameaningwithinoursufferingsupportsthewholetherapeuticventure.Byworkingtowardsunderstandingthereasonsforhisdisappointmentsthismanhadthechancetobeginreshapinghisownlifejourney.Thiswasunlikelytogivehimhappinessasagivenconstantbutcouldenablehimtodevelopsomethingfarmoreimportant.AsC.G.JungthefounderofAnalyticalPsychologysaid:Theprincipalaimofpsychotherapyisnottotransportthepatienttoanimpossiblestateofhappinessbuttohelphimacquiresteadfastnessandphilosophicpatienceinthefaceofsuffering.Lifedemandsforitscompletionandfulfillmentabalancebetweenjoyandsorrow. Itisausualeasewithhappinessthat
下列关于反常积分的命题①设fx是-∞+∞上的连续奇函数则②设fx在-∞+∞上连续且存在则必收敛且③若都发散则不能确定是否收敛④若都发散则不能确定是否收敛中是真命题的个数有
下列命题不正确的是
Therehasbeenadiscussionrecentlyontheissueinanewspaper.Writeanessaytothenewspaperto 1showyourunderstandingofthesymbolicmeaningofthepicturebelow 2giveaspecificexampleand 3giveyoursuggestionastothebestwaytoshowlove. Youshouldwriteabout200wordsonANSWERSHEET2.
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