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1、APCalculusBCExamSectionI--MultipleChoiceSECTIONI,PartATime—55minutesNumberofquestions—28Acalculatormaynotbeusedonthispartoftheexam.DIRECTIONS:Solveeachofthefollowingproblems,usingtheavailablespaceforscratchwork.Afterexaminingtheformofthechoices,decidewhichisthebestofthechoic
2、esgivenandfillinthecorrespondingovalontheanswersheet.Donotspendtoomuchtimeonanyoneproblem.Inthisexam,(1)Unlessotherwisespecified,thedomainofafunctionfisassumedtobethesetofallrealnumbersxforwhichf(x)isarealnumber.(2)Theinverseofatrigonometricfunctionfmaybeindicatedusingtheinv
3、ersefunctionnotation?−?orwiththeprefix“arc”(e.g.,sin−1?=???????).1.If??=ln(1−??),then?′0=1(A)0(B)1(C)−?(D)?(E)1+2?2.Iffisadifferentiablefunctionsuchthat?(2)=9,?′2=6,whichofthefollowingstatementcouldbefalse?Alim??=9x→2Blim??=lim??x→2+x→2−??−9(C)lim=6x→2?−2?2+?−9(D)lim=6h→0?El
4、im?′?=6x→23.Thepositionofaparticlemovinginthexy-planeisgivenbythe??parametricequations??=??????=??.Whatisthe?speedoftheparticleattime?=??(A)(8,6)(B)(4,12)(C)(12,6)(D)10(E)1604.sec2(2?)??=tan2xA+C2Btan2x+CC2tan2x+Csec32xD+C3E−csc(2x)+C∞(?−1)2?5.Whatistheradiusofconvergenceoft
5、heseries?5??=05(A)25(B)5(C)5(D)5+1(E)2dy6.If?+?=???−???????,then=dx?A(1−?)1−?2?B1−?(1+?2)11C−?1−?2(21−?2−1)?D(1−?)1−?2?????E(1−?)Graphoff7.Thegraphoffisshownabovefor0≤x≤5.Whatisthevalueof0?????5(A)−7(B)−5(C)5(D)13(E)14??8.Thelengthofacurvefromx=2tox=5isgivenby?+??.??Ifthecur
6、vecontainsthepoint(1,5),whichofthefollowingcouldbeanequationforthiscurve?1A?=+4?B?=ln?+5C?=5−ln?D?=2?+31E?=+4?9.Aspacetravelerismovingfromlefttorightalongthecurve?=?2+1.Whenheshutsofftheengines,hewillcontinuetravellingalongthetangentlineatthepointwhereheisatthetime.Atwhatpoi
7、ntshouldheshutofftheenginesinordertoreachthepoint(4,16)?(A)(0,1)(B)(1,2)(C)(2,5)(D)(3,10)(E)(5,26)10.Aparticlemovesonthex-axiswithpositiongivenby??=??−????+???+??for0≤t≤8.Howmanytimesdoestheparticlechangedirectionastincreasesfrom0to8?(A)0(B)1(C)2(D)3(E)4x0123?′(x)-506911.The
8、polynomialfunctionfhasselectedvaluesofitsfirstderivative?′giveninthetableab
