微积分期中考每题十分共十题总分100分

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1、微積分期中考每題十分共十題總分100分日期:95.11.231.Findequationsfortheselinesthatistangenttothegraphoffforthegivenvalueofx.(a)(b)2.Findthegivelimitorshowitdoesnotexist.Ifthelimitisinfinite,indicatewhetheritisor-.(a)(b)(c)(d)3.Listallthevaluesofxforwhichthegivefunctionisnotcontinuous(a)(b)4.Discussthec

2、ontinuityofthefunction5.Findthederivativeofthegivenfunction(a)(b)(c)(d)6.Findforgivenvalueofx(a);forx=1(b),forx=31.Abookstorecanobtainacertaingiftbookfromthepublisheratacostof$3perbook.Thebookstorehasbeenofferingthebookatpriceof$15percopy,andatthisprice,hasbeenselling200copiesamonth

3、.Thebookstoreisplanningtoloweritspricetostimulatesalesandestimatesthatforeach$1reductionintheprice,20morebookswillbesoldeachmonth.Expressthebookstore’smonthlyprofitfromthesalesofthisbookasafunctionofthesellingprice,drawthegraph,andestimatetheoptimalsellingprice.2.Amanufacturercansel

4、lacertainproductfor$80perunit.Totalcostconsistsofafixedoverheadof$4,500plusproductioncostsof$50perunit.(a)Howmanyunitsmustthemanufacturerselltobreakeven?(b)Whatisthemanufacturer’sprofitorlossif200unitsaresold?(c)Howmanyunitsmustthemanufacturerselltorealizeaprofitof$900?3.Animportero

5、fBraziliancoffeeestimatesthatlocalconsumerswillbuyapproximatelyD(p)=poundsofthecoffeeperweekwhenthepriceispdollarsperpound.Itisalsoestimatedthattweeksfromnow,thepriceofBraziliancoffeewillbep(t)=6dollarsperpound.(a)Atwhatratewillthedemandforcoffeebechangingwithrespecttopricewhenthepr

6、iceis$9?(b)Atwhatratewillthedemandforcoffeebechangingwithrespecttotime10weeksfromnow?Willthedemandbeincreasingordecreasingatthistime?4.BeaJohnson,theowneroftheBeaNiceboutique,estimatesthatwhenaparticularkindofperfumeispricedatpdollarsperbottle,shewillsellB(p)=bottlespermonthatatotal

7、costofdollars(a)ExpressBea’sprofitP(p)asafunctionofthepricepperbottle.(b)Atwhatrateistheprofitchangingwithrespecttopwhenthepriceis$12perbottle?Isprofitincreasingordecreasingatthatprice?