% APPM$1235$Final$Exam$$Fall$2016$

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1 Name Section APPM$1235$Final$Exam$$Fall$2016$ Page Score December13,2016 ATTHETOPOFTHEPAGEpleasewriteyournameandyoursectionnumber.The followingitemsarenotpermittedtobeusedduringthisexam:textbooks,class notes,othernotesorstudymaterialsofanykind,sliderules,andelectronic devicesofanykindincludingbutnotlimitedtocalculatorsandmobile phones.anyscratchpaperusedduringthisexammustbeonlythatwhichhas beenprovidedbytheproctor(s). Do$all$your$work$on$this$exam.$$Any$work$done$on$scrap$paper$will$NOT$be$ graded.$ PartI.ShowYourWork,7problems,84points Total /12 /24 /24 /24 /36 /30 PartII.ShortAnswer,11problems,66points Total:150points PartI.ShowYourWork.Simplifyallsolutions.Methodcounts.Leaveyouranswersintermsofπasnecessary.Use intervalnotationasnecessary.pleaseboxyourfinalanswers. 1.[12points]Solve: (x + 6) 4/3 3(x + 6) 1/3 +10x(x + 6) 2/3 =0.

2 2.[12points]FromanobservationtoweraYetiatypecreature(hereafterreferredtoas theyeti ) isspottedatpointawhichis2000metersfromthetoweratanangleof60 northofdueeastas showninthefigure.theyetiisheadingdirectlysouth.35minuteslatertheyetiisspottedatpoint Bwhichisatanangleof45 northofdueeast. (a)atwhatspeedistheyetitravelingfrompointatopointb?youmayusethefollowing toobtainanapproximationoftheyeti sspeed: 2 =1.4, 3 =1.7, 1 = 0.6.Giveunitswithyouranswer. 3 1 = 0.7 and (b)atpointb,attractedbytheglintofsunlightofftheparkranger sbinoculars,theyetisuddenlyturnsandheads directlytowardtheobservationtower.iftheyeti sspeedisnow30metersperminute,howlongwillittakeforthe YetitoreachtheobservationtowerfrompointB? " 3.[12points]Findallsolutionson[0,2π): sin 2x π $ ' = 0. 8 & 2000m A B Page2

3 4.[12points]Findallsolutionson[0,2π): cos x cos2x =1. 5.[2@6pointseach]Foreachquestionbelowtherearetwocorrectanswersamongthefivechoicesgiven.Circling onecorrectanswerisworth4.5points;circlingbothcorrectanswersisworth6points.donotcirclemorethantwo answersforanyquestion.circlingmorethantwoanswersforanyquestionwillresultinzeropointsforthatquestion. (a)whichtwoofthefivechoicesbelowareequivalentto tan x 1+ tan 2 x? A.sin x cos x B.sin x cos 3 x C. tan x + cot x D. 1 sin2x E. cot x 2 (b)whichtwoofthefivechoicesbelowareequivalentto tan 2 x sin 2 x? A.sec 2 x cos 2 x B. tan 2 x sin 2 x C. sin4 x cos 2 x D. 0, π E. tan2 x + cos 2 x Page3

4 6.[12points]Afiveasidedbox(anopenbox 24 withnotop)istobeconstructedbycutting awaythecornersofasheetofcardboardand foldingupthesides.thesheetofcardboardis 16 wideby24 long.adiagramofhowthe 16 cardboardistobecutisshowntotheright. (a)findanequationforthevolumevoftheboxasafunctionofx.callthisfunctionv(x).(youmayleaveyour equationinfactoredform.) (b)sketchthegraphofv(x)ontheaxesbelowwiththezeroslabeled.thenuseyoursketchtoestimatethevalueofx atwhichthevolumeoftheboxisamaximumanduseittocomputetheestimatedmaximumvolume. 7.[12points]Findtheequationofthefunctionshown.Thedottedlinesareasymptotesofthefunction.Thezerosof thefunctionare 2and6. Page4

5 PartII.ShortAnswer[6pointseach,66pointstotal]Theseproblemswillbegradedonyouranswersonly.Giveyour answersontheblanklinesontherightsideofthepage.for$multiple$choice$questions$you$only$need$to$give$the$ letter$corresponding$to$each$correct$answer.ifananswerdoesnotexist,state DNE. 8.Solve: e x ln2 = Whichoneofthefollowingisthefunction f (x) = x inpiecewiseform? A. y = $ C. y = $ x 1 x 7 x 1 x If sint = 1,findsin(π + t) x 3 x < 3 x 2 x < 2 B. y = $ D. y = $ x 1 x +1 x + 7 x 7 x 1 x < 1 x 7 x < Whichoneofthefollowingisthedifferencequotient f (x) = x 2 5? f (x + h) f (x) h forthefunction 11. A. h 10 h B. h C. 2x D.1 E. 2x + h 12.If R(x) isarationalfunctionwithahorizontalasymptoteat y = 2,thenwhichof thefollowingmustbetrue.chooseallthecorrectanswers. A.As x, R(x) 2. B.As R(x), x 2. C.Therangeof R(x) mustbe(, 2) ( 2, ). D. R(x) doesnothaveaslantasymptote. E. R(x) = 2 hasnosolution. 13.Howmanypeaksorrelativemaximumsdoesthefunction y = sin 4x haveinthe interval[0,2π)? Page5

6 14.Trueorfalse: 20 2 x 3x ( ) = 40x 60x (Circlethecorrectanswer.) 14.True False " 15.Evaluatesin 2tan 1 2 $ ' 5& 15.! 1 16.Whichoneofthefollowingisequivalentto 2 log 5 x + log 5 $ " y & log 5 z? 16.! x 2 $ A. log 5 " y z & B. log! x 2 $ 5 " y 2 & z C. log " x 2 y 5 $ ' z &! x 2 z $ D. log 5 " y & E. log " 5$ x2 + 1 y z & 17.Whichoneofthefollowingisthegraphofof y = 25 x 2? 17. A B C D E ' ' 18.ThefollowingfunctionsallhavethesamedomainEXCEPTforone.Whichfunction hasadomainthatisdifferentfromtheothers? A. y = 1 x 8 B. y = ln(x 8) C. y = 1 x 8 D. y = x 2, x > 8 " 1 E. y = ln$ x 8& ' END$OF$EXAM$ Page6