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设函数 f (x)=acos2x+(a-1)(cosx+1),其中 a>0,记| f (x)| 的最大值为 A,

(Ⅰ)求 f '(x);

(Ⅱ)求 A;

(Ⅲ)证明 |f '(x)|≤2A

更新时间:2024-04-28 00:33:30
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3

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_____yourtimelyadvice,Iwouldneverhaveknownhowtogoaboutthework.

Thecountry’schiefexportsarecoal,carsandcottongoods,cars_____themostimportantofthese.

Iwastohavemadeaspeechif_____.

Passage2

Questions6to10arebasedonthefollowingpassage:

Whenaluminumwasfirstproducedaboutahundredandfiftyyearsago,itwassodifficulttoseparateformtheoresinwhichitwasfoundthatitspricewashigherthanthatofgold.Thepriceremainedhighuntilanewprocesswasdiscoveredforrefiningthemetalwiththeaidofelectricityapproximatelythreequartersofacenturylater.Thenewmethodwassomuchcheaperthataluminumbecausepracticalformanypurposes,oneofwhichwasmakingpotsandpans.

Aluminumislightweight,rustproofandeasilyshapedintodifferentforms.Bymixingitwithothermetals,scientistshavebeenabletoproduceavarietyofalloys,someofwhichhavethestrengthofsteelbutweighonlyonethirdasmuch.

Today,theusesofaluminumareinnumerable.Perhapsitsmostimportantuseisintransportation.Aluminumisfoundintheengineofautomobiles,inthehullsofboats.Itisalsousedinmanypartsofairplanes.Infact,thehuge“airbus”planeswouldprobablyneverhavebeenproducedifaluminumdidnotexist.Bymakingvehicleslighterinweightaluminumhasgreatlyreducedtheamountoffuelneededtomovethem,Aluminumisalsobeingusedextensivelyinthebuildingindustryinsomecountries.

Sincealuminumissuchaversatile(多用的)metal,itisfortunatethatbauxite(铝土矿),whichisoneofitschiefsources,isalsooneoftheearth’smostplentifulsubstances.Asthesourceofaluminumisalmostinexhaustible,wecanexpectthatmoreandmoreuseswillbefoundforthisversatilemetal.

6.Thepriceofaluminumwassharplyreducedwhenpeoplediscoveredanewrefiningprocesswiththeaidof.

A.windB.solarenergyC.hydraulicpowerD.electricity

7.Aluminumis.

A.lightweight,rustproofbutnoteasilyshapedintodifferentforms

B.heavyweight,rustproofandeasilyshapedintodifferentforms

C.lightweight,rustproofandeasilyshapedintodifferentforms

D.lightweightandeasilyshapedintodifferentformsbutitiseasytobecomerusty

8.WhichofthefollowingisNOTtrue?

A.Aluminumiswidelyusedintransportation.

B.Aluminumisalsousedinmanypartsofairplanes.

C.Aluminumisbeingusedextensivelyinthebuildingindustry.

D.Aluminumisnotusedinitspureform.

9.Aluminumisfoundonearthmostlyintheformof.

A.puremetalB.bauxiteC.goldD.liquid

10.Whatisthepassagetalkingabout?

A.Thefeaturesofaluminumanditsfunctions.B.Theprocessofaluminum.

C.Thediscoveryofaluminum.D.Thepromisingfutureofaluminum.

PASSAGETWO

(1)TheNobelsaretheoriginals,ofcourse.AlfredNobel,themanwhoinventeddeadlyexplosives,decidedtotryanddosomethinggoodwithallthemoneyheearned,andgaveprizestopeoplewhomadeprogressinliterature,science,economicsand—perhapsmostimportantly—peace.

(2)NotallrewardsareasnobleastheNobels.Eventhoughmostcountrieshaveasystemofrecognizing,honoringandrewardingpeoplewhohavedonesomethinggoodintheircountries,therearenowhundredsofawardsandawardceremoniesforallkindsofthings.

(3)TheOscarsareprobablythemostfamous,atimeforthe(mostly)Americanfilmindustrytotellitselfhowgooditisandanannualopportunityforlotsofbigstarstogiveeachotherawardsandmaketearfulspeeches.AswellasthattherearealsotheGoldenGlobes,evidentlyforthesamething.

(4)Butit’snotonlyfilms---therearealsoGrammies,Brits,theMercuryPrizeandtheMTVformusic.InBritain,awriterwhowinstheBookerPrizecanexpecttoseetheirdifficult,literarynovelhitthebestsellerlistsandcompetewiththeDaVinciCodeforpopularity.TheTurnerPrizeisanawardforBritishcontemporaryartists—eachyearitcausescontroversybyapparentlygivinglotsofmoneytoartistswhodothingslikedisplayingtheirbeds,puttinganimalsinglasscasesor—thisyear—buildingagardenshed.

(5)Awardsdon’tonlyexistforarts.TherearenowawardsforSportsPersonalityoftheYear,forEuropeanFootballeroftheYearandWorldFootballeroftheYear.Thisseemsverystrange—sometimesawardscanbegoodtogiverecognitiontopeoplewhodeserveit,ortohelppeoplewhodon’tmakealotofmoneycarryontheirworkwithoutworryingaboutfinances,butprofessionalsoccerplayersthesedayscertainlyaren’tshortofcash!

(6)Manysmalltownsandcommunitiesallovertheworldalsohavetheirownawardceremonies,forlocalwritersorartists,orjustforpeoplewhohavegraduatedfromhighschoolor,gotauniversitydegree.EventheBritishCouncilhasitsownawardsfor“InnovationinEnglishLanguageTeaching”.

(7)Whyhavealltheseawardsandceremoniesappearedrecently?Shakespeareneverwonaprize, nordidLeonardoDaVinciorAdamSmithorCharlesDickens.

(8)Itwouldbepossibletosay,however,thatinthepast,scientistsandartistscouldwin“patronageformrichpeople”—akingoralordwouldgivetheartistsorscientistsmoneytohavethempainttheirpalacesorhelpthemdevelopnewwaysofmakingmoney.Withthechangeinsocialsystemsacrosstheworld,thisnolongerhappens.Alotofscientificresearchisnoweitherfundedbythestateorbyprivatecompanies.

(9)Perhapsawardceremoniesarejustthemostrecentphaseofthisprocess.

(10)However,thereismoretoitthanthat.WhenafilmwinsanOscar,manymorepeoplewillgoandseeit,orbuytheDVD.WhenawriterwinstheNobelPrize,manymorepeoplebuytheirbooks.WhenagroupwinstheMTVawards,theceremonyisseenbyhundredsofthousandsofpeopleacrosstheworld.Theresult?Thegroupsellslotsmorerecords.(11)Mostawardceremoniesarenowsponsoredbybigorganizationsorcompanies.Thismeansthatitisnotonlythepersonwhowinstheawardwhobenefits---butalsothesponsors.TheMTVawards,forexample,aregreatforpublicizingnotonlymusic,butalsoMTVitself!

(12)Onthesurface,itseemstobea“Win-win”situation,witheveryonebeinghappy,butletmeaskyouaquestion—howfardoyouthinkthatpublicityandmarketingarewinninghere,andhowmuchgenuinerecognitionofachievementistakingplace?

1.Whatistheauthor’stonewhenhementionsawardssuchastheOscars,theGoldenGlobesand

Grammies(Paras.3&4)

A.Amused.

B.Appreciative.

C.Sarcastic.

D.Serious.

2.AccordingtoPara.4,whatwouldhappentoawardwinningwriters?

A.Theywouldenjoyamuchlargerreadership.

B.Theywouldturntopopularnovelwriting.

C.Theywouldcontinuenon-fictionwriting.

D.Theywouldtrycontroversialformsofart.

3.WhichofthefollowingstatementsbestsumsupPara.6?

A.Awardsceremoniesareheldforlocalpeople.

B.Awardsceremoniesareheldonimportantoccasions.

C.Awardsceremoniesareheldincertainprofessions.

D.Awardsceremoniesareheldforallsortsofreasons.

4.AccordingtoPara.8,onedifferencebetweenscientistsandartistsinthepastandthoseatpresent

liesin_____________.

A.natureofwork

B.personalcontact

C.sourceoffunding

D.socialstatus

5.ItcanbeconcludedfromPara.12thattheauthorthinksawards________.

A.promotemarketratherthanachievements

B.dogoodtobothmarketandpopularity

C.helpthosewhoarereallytalented

D.areeffectiveinmakingpeoplepopular

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