第1題Leibnizcalledboth

???

and

????

“di?erentials”.第1題Attimetseconds,thecenterofabobbingcorkisy=2sintcentimetersabove(orbelow)waterlevel.Thenthevelocityofthecorkatt=

πis

____正確答案：:-21.2homework第1題Awheelcenteredattheoriginandofradius10centimetersisrotatingcounterclockwiseatarateof4revolutionspersecond.ApointPontherimisat(10,0)att=0.ThenthecoordinatesofPattime10secondsare____,therateatwhichPrisingattimet=1is____π.正確答案：:(10,0)正確答案：:801.3homework第1題Anobjectthrowndirectlydownwardfromthetopofacliffwithaninitialvelocityof

v0feetpersecondfalls

intseconds.Ifitstrikestheoceanbelowin3secondswithaspeedof140feetpersecond,howhighisthecliff?____

feet.正確答案：:2761.4homework第1題Ametaldiskexpandsduringheating.Ifitsradiusincreasesattherateof0.02inchpersecond,howfastistheareaofoneofitsfacesincreasingwhenitsradiusis8.1inches?

____πin.^2/s正確答案：:0.324/1.0181.5homework第1題Bydifferential,theapproximationsto4.1is

____正確答案：:2.025第2題Poiseuille'sLawforbloodflowsaysthatthevolumeflowingthroughanarteryisproportionaltothefourthpoweroftheradius,thatis,V=kR4.Byhowmuchmusttheradiusbeincreasedinordertoincreasethebloodflowby40%?

____正確答案：:10%1.8homework第1題Ineconomics,dRdxiscalled____

,dPdx

iscalled____正確答案：:marginalrevenue正確答案：:marginalprofit第2題Inmanufacturingandsellingxunitsofacertaincommodity,thepricefunctionpandthecostfunctionC(indollars)aregivenbyp(x)=5.00?0.002xC(x)=3.00+1.10xWhenx=____thatwillproducethemaximumtotalprofit.正確答案：:9751.9homework第1題Iffis____

onaclosedinterval[a,b]anddifferentiableon

____,thenthereisatleastonenumbercin(a,b)where

f(b)?f(a)=f′(c)(b?a)正確答案：:continuous正確答案：:(a,b)2.5homework第1題A62feetwidehallwaymakesaright-angleturn.Whatisthelengthofthelongestthinrodthatcanbecarriedaroundthecornerassumingyoucannottilttherod?____feet正確答案：:243.1homework第1題Iftwosolidswithbasesinthesameplanehavecrosssectionsofthesameareainallplanesparalleltotheirbases,thentheyhavethesamevolume.第2題∫?11(x9+sin3x)dx=____正確答案：:0第3題LetRbetheregionboundedbyx=2y,y=2,y=6andx=0.ThevolumeofthesolidobtainedwhenRisrevolvedaboutthey-axisis2π3.3.3homework第1題Mouhefanggaiisthesolidregioncommontotworightcircularcylindersofradiusrwhoseaxisintersectatrightangles.Thetotalvolumeofmouhefanggaiis

3.4homework第1題Anobjectofmass4isatx=1andasecondobjectofmass6isatx=3.Simplegeometricintuitiontellsusthatthecenterofmasswillbetothe

____ofx=2.Infact,itisat

=____正確答案：:right正確答案：:2.2第2題Thehomogeneousrectangularlaminawithcornerpoints(0,0),(2,0),(2,6)and(0,6)willbalanceat

=____,=____正確答案：:1正確答案：:33.8homework第1題Arandomvariablewhosesetofpossibleoutcomesisfiniteorcanbeputintoaninfinitelistiscalleda

____randomvariable.Arandomvariablewhosesetofpossibleoutcomesmakesupanintervalofrealnumbersiscalleda

____randomvariable.正確答案：:discrete正確答案：:continuous第2題Fordiscreterandomvariables,probabilitiesandexpectationsarefoundbyevaluatinga(an)

____,whereasforcontinuousrandomvariables,probabilitiesandexpectationsarefoundbyevaluatinga(an)

____.正確答案：:sum正確答案：:integral第3題IfacontinuousrandomvariableX

takesonvaluesin[0,20]andhasPDFf(x),thenP(x≤5)isfoundbyevaluating

∫05f(x)dx第4題Theaccumulationfunction

∫Axf(t)dt,whichaccumulatestheprobability(areaunderthePDF),iscalledthe

____.

正確答案：:cumulativedistributionfunction3.9homework第1題Ifthenaturallengthofaspringis0.2meter,andifittakesaforceof12Newtonstokeepitextended0.04meter,theworkdoneinstretchingthespringfromitsnaturallengthtoalengthof0.3meteris1.2joules.3.10homework第1題IfaninitialamountofA0dollarsisdepositedinabankpayinganinterestrateofrperyearcompoundedcontinuously,thefuturevalueofthismoneyisgivenbytheformulaFuturevalue

第2題IfoneaimstoobtainanamountofA0

dollarstyearsdowntheroadfromanaccountthataccruesinterestattheannualrateofr,thenthepresentvalueforthisamount,i.e.,theamountofmoneythatoneneedstoputintodayisPresentvalue=A0ert.

3.11homework第1題Ifa1000-poundcapsuleweighsonly165poundsonthemoo