Microsoft Word - 3A, Exam 3.docx 3A,Exam3 XXXXXXXXXX)WeissS21 NAME:________________________________________________ 100points SCORE: ___________%...

Calculus HW problems


Microsoft Word - 3A, Exam 3.docx 3A,Exam3(3.5-4.2)WeissS21NAME:________________________________________________ 100pointsSCORE:___________% HONORCODE:AllworkIsubmitismyown;Iwillnotshareanswers.Initials:_______ Latepolicy:5%offforeach15minutestheexamislate(startingat12:15pm) Showallofyourworkforfullcredit.GOODLUCK!☺ 1.(9points)Theheightsofaflarefiredfromthemoon’ssurfaceisgivenbythe function � s = −0.81t2 + 121.5t ,wheresisinmetersandtissecondsafterfiring. Roundfinalanswersto1decimalplaceandshowallofyourwork. a)Inhowmanysecondsafterfiringwilltheflarehaveavelocityof89.1m/sec? b)Inhowmanysecondsafterfiringwilltheflarelandonthemoon’ssurface? c)Findthespeed(notvelocity)oftheflarewhenitlandsonthemoon’ssurface. 2.(7points)Findthefirstandsecondderivativesofthefunction � y = tanx + e5x � y ' = y ' ' = 3.(16points)Findthederivativeofeachfunction.Leaveunsimplifiedanswers. a) � y = 3−x b) � y = lnx cotx c) � y = 3x tan−1(x) d) � y = (7x3 + 6x2)50 4.(8points)Findtheequationofthetangentlineto � f (x) = cos−1 x atthepointon thegraphofwherex=0.MakesureyourcalculatorisinRadianmode.Answerin slope-interceptform,usingexactvalues,notdecimals.Showallwork. In#5and6findthederivativeofthefunction.Leaveunsimplifiedanswers,please. 5.(3points) � y = ln 8x5 − 2x2 + 7( ) 6.(5points) � y = log6(x) + cot−1(x5) 7.(11points)Useimplicitdifferentiationtoisolate � ′ y (or � dy dx ifyoupreferthatform) � 2x + x4y + y3 = cos(x) − 9 . 8.(13points)Uselogarithmicdifferentiationtofind � ′ y for � y = (x 6 + 1) 1 2(sin5 x) (x − 9)12 Showallalgebraandcalculusstepsclearly.Donotleaveyinthefinalanswer. 9.(5points)Airisleakingoutofasphericalballoon,andtheballoon’svolumeis decreasingatarateof � −50 in3 /min. Howfastistheradiusoftheballoonchangingwhentheradiusis5inches? Usethevolumeformula � V = 4 3 πr3 .Leaveyouranswerinexactform(withπ). 10.(7points)Thesidesofarighttrianglewithlegsa,b,andhypotenusecareall expanding,withgivenrates � da dt = 2cm/sec and � db dt = 1.5cm/sec .Atwhatrateis thehypotenusecexpandingwhena=3cmandb=4cm?Roundto1decimalplace. 11.(11points)Usecalculus(notagraph)tofindtheabsolutemaximumand absoluteminimumy-valuesof � y = 4x4 − 8x3 ontheclosedinterval [–1,3].Showallwork. 12.(5points)Findthevalueofcintheinterval � −1,0[ ] thatsatisfiestheconclusion ofRolle’sTheoremforthecontinuousanddifferentiablefunction � f (x) = x3 − x + 2.