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电大经济数学基础12复习资料考试小抄
一、单项选择题1.下列函数中为偶函数的是(). A B C D正确答案A2.下列函数中为奇函数的是(). A B C D正确答案B3.下列各函数对中,()中的两个函数相等.A.B.C.D.正确答案D4.下列结论中正确的是().A周期函数都是有界函数B基本初等函数都是单调函数C奇函数的图形关于坐标原点对称D偶函数的图形关于坐标原点对称正确答案C5.下列极限存在的是().A.B. C. D.正确答案A6.已知,当()时,为无穷小量.A.B.C.D.正确答案A7.当时,下列变量为无穷小量的是()A.B.C.D.正确答案D8.函数在x=0处连续,则k=.A.-2B.-1C.1D.2正确答案B
9.曲线在点处的切线斜率是().A B C D正确答案D 10.曲线在点
(01)处的切线斜率为()A.B.C.D.正确答案B11.若,则().A.0B.1C.4D.-4正确答案C12.下列函数在区间上单调减少的是().ABCD正确答案B 13.下列结论正确的是().A若,则必是的极值点B使不存在的点,一定是的极值点C是的极值点,且存在,则必有D是的极值点,则必是的驻点正确答案C14.设某商品的需求函数为,则当时,需求弹性为().A.B.-3C.3D.正确答案B15.若函数,则.A.-2B.-1C.-
1.5D.
1.5正确答案A16.函数的连续区间是().A.B.C.D.正确答案A17.设,则=().A.B.C.D.正确答案C18.下列积分值为0的是().A.B.C.D.正确答案C19.若是的一个原函数,则下列等式成立的是.A.B.C.D.正确答案B
20.设,,是单位矩阵,则=().A.B.C.D.正确答案A
21.设为同阶方阵,则下列命题正确的是(). A.若,则必有或B.若,则必有 C.若秩秩,则秩D.正确答案B22.当条件()成立时,元线性方程组有解.A.B.C.D.正确答案D
23.设线性方程组有惟一解,则相应的齐次方程组().A.无解B.只有0解C.有非0解D.解不能确定正确答案B
24.设线性方程组的增广矩阵为,则此线性方程组的一般解中自由未知量的个数为().A.1B.2C.3D.4正确答案B
25.若线性方程组的增广矩阵为,则当=( )时线性方程组无解.A B CD正确答案A
26.设,则( ).A B C D正确答案D
27.设线性方程组有无穷多解的充分必要条件是().A.B.C.D.正确答案B28.设线性方程组有唯一解,则相应的齐次方程组().A.只有零解B.有非零解C.无解D.解不能确定正确答案A
29.设A为矩阵,B为矩阵,则下列运算中()可以进行.A.ABB.ABTC.A+BD.BAT正确答案A
30.设是可逆矩阵,且,则().A.B.C.D.正确答案C
31.设需求量q对价格p的函数为则需求弹性为Ep=A.B.C.D.正确答案D
32.在无穷积分中收敛的是()A.B.C.D.正确答案C
33.设A为3×4矩阵B为5×2矩阵且乘积矩阵有意义则C为矩阵.A.4×2B.2×4C.3×5D.5×3正确答案B
34.线性方程组的解的情况是()A.无解B.只有0解C.有唯一解D.有无穷多解正确答案A
二、填空题1.函数的定义域是 .正确答案2.函数的定义域是 .正确答案3.若函数,则.正确答案4.设,则函数的图形关于 对称.正确答案y轴5.已知需求函数为,则收入函数=.正确答案6. .正确答案17.已知,若在内连续,则.正确答案28.曲线在处的切线斜率是 .正确答案9.过曲线上的一点(0,1)的切线方程为.正确答案10.函数的驻点是 .正确答案11.设,当 时,是对称矩阵.正确答案112.已知,当时,为无穷小量.正确答案13.齐次线性方程组(是)只有零解的充分必要条件是 .正确答案14.若,则=.正确答案15.= .正确答案16.设线性方程组,且,则时,方程组有唯一解.正确答案17.设齐次线性方程组,且=rn,则其一般解中的自由未知量的个数等于.正确答案n–r18.线性方程组的增广矩阵化成阶梯形矩阵后为则当= 时,方程组有无穷多解.正确答案-
119.已知齐次线性方程组中为矩阵,则.正确答案
320.函数的间断点是 .正确答案
21.若,则 .正确答案
三、微积分计算题1.已知,求.解由导数运算法则和复合函数求导法则得2.设,求.解;3.设,求.解由导数运算法则和复合函数求导法则得4.设,求.解由导数运算法则和复合函数求导法则得5.解===6.计算解7.计算解8.计算解9.计算解==10.计算解=11.解===12.解=-==13.====1
四、代数计算题1.设矩阵,求.解因为 即 所以 2.设矩阵,是3阶单位矩阵,求.解由矩阵减法运算得利用初等行变换得 即
3.设矩阵A=,B=,计算AB-1.解因为AB==ABI=所以AB-1=
4.解矩阵方程解由,得所以,5.求线性方程组的一般解.解因为系数矩阵所以一般解为(其中,是自由元)6.当取何值时,线性方程组有解?并求一般解.解因为增广矩阵所以,当=0时,线性方程组有无穷多解,且一般解为是自由未知量〕
五、应用题1.投产某产品的固定成本为36(万元),且边际成本为(万元/百台)试求产量由4百台增至6百台时总成本的增量,及产量多少时,可使平均成本达到最低?当产量由4百台增至6百台时,总成本的增量为(万元)又令,解得2.已知某产品的边际成本(万元/百台),为产量(百台),固定成本为18(万元),求最低平均成本.解总得成本函数为平均成本函数为,令,解得(百台)因为平均成本存在最小值,且驻点唯一,所以,当产量为300台时,可使平均成本达到最低最低平均成本为(万元/百台)3.生产某产品的边际成本为万元/百台,边际收入为(万元/百台),其中x为产量,问1产量为多少时,利润最大?2从利润最大时的产量再生产2百台,利润有什么变化?解
(1)边际利润函数为令得(百台)又是的唯一驻点,根据问题的实际意义可知存在最大值,故是的最大值点,即当产量为10(百台)时,利润最大.
(2)利润函数即从利润最大时的产量再生产2百台,利润将减少20万元.4.已知某产品的边际成本(元/件),固定成本为0,边际收益问产量为多少时利润最大?在最大利润产量的基础上再生产50件,利润将会发生什么变化?解因为边际利润令,得是唯一驻点,而该问题确实存在最大值所以,当产量为500件时,利润最大当产量由500件增加至550件时,利润改变量为即利润将减少25元
5.设生产某产品的总成本函数为万元,其中x为产量,单位百吨.销售x百吨时的边际收入为(万元/百吨),求1利润最大时的产量;2在利润最大时的产量的基础上再生产1百吨,利润会发生什么变化?解1因为边际成本为,边际利润令,得由该题实际意义可知,为利润函数的极大值点,也是最大值点.因此,当产量为7百吨时利润最大.2当产量由7百吨增加至8百吨时,利润改变量为(万元)即当产量由7百吨增加至8百吨时,利润将减少1万元6.设生产某种产品个单位时的成本函数为(万元)求⑴当时的总成本和平均成本;⑵当产量为多少时,平均成本最小?解⑴因为总成本、平均成本和边际成本分别为,所以,,⑵令,得(舍去),可以验证是的最小值点,所以当时,平均成本最小
7.某厂每天生产某种产品件的成本函数为(元).为使平均成本最低,每天产量应为多少?此时,每件产品平均成本为多少?解因为==()==令=0,即=0,得=140,=-140(舍去)=140是在其定义域内的唯一驻点,且该问题确实存在最小值所以=140是平均成本函数的最小值点,即为使平均成本最低,每天产量应为140件.此时的平均成本为==176(元/件)8.已知某产品的销售价格(单位元/件)是销量(单位件)的函数,而总成本为(单位元),假设生产的产品全部售出,求产量为多少时,利润最大?最大利润是多少?解由已知条件可得收入函数利润函数求导得令得,它是唯一的极大值点,因此是最大值点.此时最大利润为即产量为300件时利润最大.最大利润是43500元.
9.设生产某种产品个单位时的成本函数为(万元)求⑴当时的总成本和平均成本;⑵当产量为多少时,平均成本最小?解⑴因为总成本、平均成本和边际成本分别为;,所以,;,⑵令,得(舍去),可以验证是的最小值点,所以当时,平均成本最小.
10.设生产某产品的总成本函数为万元,其中为产量,单位百吨.销售百吨时的边际收入为(万元/百吨),求⑴利润最大时的产量;⑵在利润最大时的产量的基础上再生产百吨,利润会发生什么变化?解⑴因为边际成本为,边际利润令,得可以验证为利润函数的最大值点.因此,当产量为百吨时利润最大.⑵当产量由百吨增加至百吨时,利润改变量为(万元)即利润将减少1万元.
11.某厂生产某种产品q件时的总成本函数为,单位销售价格为,问产量为多少时可使利润最大?最大利润是多少?解设产量为q,则收入函数为因为边际利润时,利润最大则,得产量为250时可使利润最大最大利润为1230元请您务必删除一下内容,O∩_∩O万分谢谢!!!2015年中央电大期末复习考试小抄大全,电大期末考试必备小抄,电大考试必过小抄IndonesiahasemergedasatopvacationdestinationforChinesethissummeralongwithThailandsPhuketislandandtheMaldivesarchipelago.EncouragedbygrowthinChinesetravelerstoIndonesiathegovernmentinJakartahasrecentlyrelaxeditsvisapolicy.SinceJune10ChinesetouristscanenterIndonesiathroughnineappointedlocationsincludingtheSoekarnoHattaInternationalAirportinJakartatheNgurahRaiInternationalAirportinBaliandtheKualaNamuInternationalAirportinMedanbyjustgettingtheirpassportsstampedonarrival.Officiallyitiscalledthefree-visascheme.ThenewpolicyalsomeansChinesetouristscansave$35onvisafeeswhichwilllikelymaketripstoIndonesiamorealluring.WhilesuchanarrangementallowsChinesevisitorstostayupto30daysforthepurposeoftravelingthoseseekingextensionswillneedtogetpaidvisasfromthatcountrysmissionsinBeijing Shanghai Guangzhou or HongKongaccordingtoanofficialattheIndonesiaembassyinBeijing.SantoDarmosumartoheadoftheembassysinformationsocialandculturalsectionsaysthenewpolicyisaimedatstrengtheningpeople-to-peoplecontactsbetweenthetwocountries.DaiYumarketingdirectorofCtripamajorChineseonlinetravelagencysays:Weveseenanearly50percentgrowthoverthepreviousmonthinthenumberofChinesetouriststoBalisincethepolicywasannounced.DuringhistriptoChinainMarchIndonesianPresidentJokoWidodoproposedthathiscountryandChinaaimtoincreasetwo-wayvisitstoamaximumof10millionpeopleinthenextfewyears.TheIndonesiangovernmenthassettheirsightsongreeting2millionChinesetouristsbytheendofthisyearaccordingtotheofficial.TheIndonesiangovernmenthopesthatIndonesiannationalswouldalsobegivenpreferentialtreatmentwhilevisitingChinasaysDarmosumarto.In2013thenumberofChinesetouristswhovisitedIndonesiastoodaround
807000.Lastyearitincreasedto959000headds.BaliremainsthemostpopularsiteamongChinesetourists.InFebruarymorethan92200ChinesetouristsmadetripstoBalirankingfirstamongoverseasvisitorstheBaliTimesreported.Lastyeartheislandwitnessedmorethan586000arrivalsfromChinaanincreaseof51percentover
2013.BaliisntjustforsightseeingbutalsoforweddingshoneymoonsgolfandmanyoutdooractivitiessaysFanWenqingamarketingexecutiveatGarudaIndonesiasnationalairliner.GarudaoffersthreenonstopflightsbetweenBeijingandBaliandfoureachweekbetweenBeijingandJakarta.TherearedailyflightsfromGuangzhouin Guangdong provinceandShanghaitoJakartaaswell.IttakesfromsixtoeighthoursonanonstopflighttoreachIndonesiafromChina.Indonesiaishometomorethan17000islands.TouristscantourYogyakartatoseePrambanamandBorobudurtwohistoricalandreligioussitesandexplorethelocalhandicraftmarkets.ThebaseofavolcanoBandungwhichisalsoknownastheParisofJavaisidealforadventure-seekers.ManyecotourismdestinationssuchasTobaLakeinSumatraTanjungPutingNationalParkinKalimantanandBunakeninManadoareplacestheembassyofficialrecommendsfortourists.Indonesiaboastsworld-classsurfingfacilitiesalongtheshoresofSumatradowntoNusaTenggaraIslands.RecentlyLombokasisterislandeastofBalihasgottensomuchattentionfromChinesetravelersthatsometravelagenciesareofferingtwinpackagesforBaliandLombok.ThebesttimetovisitBaliisfromMaytoOctoberwhenitdoesnt rain muchandtheweatheriscool.AtpresstimeaweeklongpackagefromShanghaiorGuangzhoutoBaliwasalittlemorethan3000yuan$480onCtripswebsite.ChinesetouristshavetakenashinetoraftinginUbudsightseeinginTanahLotandsurfinganddivinginNusaLembongansaysDai.CivetcoffeeessentialoilandwoodcarvingsareamongthemostpopularproductsforChinesetouristsinIndonesiashesays.Indonesianfoodisalsosomethingthatvisitorsshouldntmiss.Localcuisinesfeaturemanyspicesincludingpeppersandclovesandcoconutpulp.Friedricedirtyduckandroastsucklingpigarerecommended.Childrensillustrationbooksfirstappearedinthe1600sinEurope.TheirpassagetoChinahowevertookmuchlongerroughly300years.InChinachildrensillustrationbookshaveahistoryofjust100yearsandtheirdevelopmentcanbedividedintofourstages.Fromearly1900stomid1900salargenumberofbooksandmagazineswithillustrationsappearedwiththefastdevelopmentofthemodernpublishingindustry.Theillustration artsatthattimewereamixedgenreofChinesetraditional paintingsandthewestern styleandmostofthestoriesoriginatefromthefundamentalchangesthatChinaexperiencedafterthecollapseofQingDynasty1644-1911thewarlordstrugglesandthewaragainsttheJapaneseinvasion.Thesecondstagewasfrommid1900stolate1970swhentheculturalrevolution1966-76ended.Thefastdevelopmentofsomespecialpublishinghousesforchildrengavebirthtoalargenumberofillustration-storybookswhichmadeagooduseoffolkarttechniquessuchaswoodboardcarvingfrescoesandinkandwashpaintingetc.ManyofthepopularstoriesarefromChinesehistoryandwarsafter1900s.Thethirdstageisfromearly1980stolate1990sagoldenperiodforthedevelopmentofchildrensillustrationbooks.Thereformandopening-upbroughtinnewconceptsandideasfromtheWesttoChinaacountrythathadbeenclosedtotheWestfornearlythreedecades.Fastdevelopmentofeconomysocietyandcultureprovidedthewritersandpainterswithalotofinspirationtocreatenewliteratureworksanddrawillustrations.ChinaalsoimportedlargeamountsofchildrensillustrationbooksfromtheWestandJapan.ManyyoungparentsinChinahaveastrongnostalgiaaboutchildrensillustrationbookstheyreadinthe1980sand1990s.ThisisalsothelasterainChinasartisticinnovationbeforetheadventoftheInternetperiod.ThefourthstageisfeaturedwiththespreadoftheInternetandtheothercomputerizedmeansofartinnovation.Thehand-drawnchildrensillustrationbooksaregraduallyreplacedbycartoonsdrawnandcopiedbysoftwareandmachinesandshownontabletscomputerstelevisionandsmartphonesinsteadofbooks.HainanTropicalWildlifeParkandBotanicalGardenisnatureshavenwithnolessthan4000rarebirdsandanimalsrepresenting200species.Withtropicalforestcoveringover90percentofitsareathegardenoffersbeautifulviewsofawiderangeoftropicalplantsflowersandfruittrees.Thescenicspotabout25kilometersfromthecenterofHaikouoffersadrive-thrusafaritourwhereyoucangetupclosewithelephantslionsandbears.TheSafarionFootareafeatureswalkingtrailswherevisitorscanseetherestoftheanimalsincludinghipposandmonkeysandfeedthemforasmallfee.Visitorsalsocanseewhathappenswhenyoubreedalionandatiger.Twouniqueattractionsarerarehybrids:aligertheoffspringofamallionandafemaletigerandatigonwhichiscreatedbyafemalelionandamaletiger.Asa teachingcenteroftheNationalPopularScienceEducationprogramtheparkalsoservesasasecondclassroomforstudentstolearnaboutwildlifeandplants.Sinceitwasestablishedin1995ithasreceivedmorethanonemillionstudentvisitors.AtacrucialmomentwhenpessimismhasbroughttheGreekcrisistosuchaheadthatthecountryisclosertoadefaultonitsdebtrepaymentsthaneverLiofferedasparkofenthusiasmtorestartthestalledtalksbycallingonGreeceanditscreditorstoreachalast-minutedealthatwillallowGreecetoremainintheeurozone.GiventheescalationofthecountryscrisisovertheweekendsentashockwavethroughtheglobalstockmarketsonMondaythereareamplereasonstoworryabouttheuncertaintiessurroundingtheeventsinGreeceandtheeffectadefaultwouldhaveonEuroperelationsbetweenChinaandtheEUglobalfinancialstabilityandthenascentglobaleconomicrecovery.Greecehasannouncedthatitwillholdareferendumonabailoutplanproposedlastweekbythecountryscreditors.InresponseGreeceseurozonepartnershaverefusedtoextendthecountrysbailoutprogramandtheEuropeanCentralBankcappeditsemergencysupportforthecountrysbanks.ArealdangernowloomsofGreeceexitingtheeurowhichmightderailtheglobaleconomicrecoveryanddamagethelong-termviabilityoftheeuroasacurrency.Howeversuchatragedyisneithercertainnorunavoidable.TheEUshouldshoulderitsresponsibilitytopreventtheGreekcrisisfromovershadowingthefragileglobalrecovery.Asamajorcustomerandsupplierofthe28-nationEUandaresponsiblelong-termholderofEurobondsChinasconfidenceinandcommitmenttoastrongeurozoneoffersEUleadersthenecessarysupporttolookattheGreekcrisisfromabroaderandlongerperspective.WhenLisaidthatChinawillnotonlyconsideraChina-EUinvestmentplatformtobackEuropeanCommissionPresidentJean-ClaudeJunckersplantorevivetheEuropeaneconomybutalsobuymorebondsissuedbytheEuropeanInvestmentBankEUleadersshouldbeclearthatChinawantstoseetheEUmaintainitsintegrityandaforwardtrajectory.Suchaconfidence-buildingeffortisparticularlyvaluableespeciallyfromsuchalargecountryasChinawhichalreadyhasahugestakeandseekstofurtherexpanditinastrongeurozone.ItwillbeatragedytoallowinactionovertheGreekcrisistostandinthewayofgrowth-boostingSino-EUcooperation.LikeashiningpearlWestLakeisthesymbolofHangzhoucity.Fromancienttimesmanypoemshavepraisedtheamazingsceneryofthelake.AttheverybeginningtheWestLakewasapartoftheQiantangRiver.Intheyear822BaiJuyiafamouspoetandanofficeroftheTangDynastyAD618-907suggestedtobuildastrongercausewaytostorewatersothatthelakewasdoubledinsize.AndduringtheSongDynastyAD960-1279manytemplesandpagodaswerebuiltduetoaBuddhistrevivalandthelookofWestLakewasformedatthattime.TheWestLakeisquitebigandfeaturesdifferentclassicviewsfromdifferentlocations.TechnicallytherearetensceneswhichweremarkedbyEmperorQianlongwithfour-characterinscriptions200yearsagosuchastheMeltingSnowontheBrokenBridgeandSunsetGlowoverLeifengPagoda.。