雨课堂学堂在线学堂云《Applications of Calculus（浙江理工）》单元测试考核答案

第1题Leibnizcalledboth

∆𝑥

and

𝑑𝑥

“differentials”.第1题Attimetseconds,thecenterofabobbingcorkisy=2sintcentimetersabove(orbelow)waterlevel.Thenthevelocityofthecorkatt=

πis

____正确答案：:-21.2homework第1题Awheelcenteredattheoriginandofradius10centimetersisrotatingcounterclockwiseatarateof4revolutionspersecond.ApointPontherimisat(10,0)att=0.ThenthecoordinatesofPattime10secondsare____,therateatwhichPrisingattimet=1is____π.正确答案：:(10,0)正确答案：:801.3homework第1题Anobjectthrowndirectlydownwardfromthetopofacliffwithaninitialvelocityof

v0feetpersecondfalls

intseconds.Ifitstrikestheoceanbelowin3secondswithaspeedof140feetpersecond,howhighisthecliff?____

feet.正确答案：:2761.4homework第1题Ametaldiskexpandsduringheating.Ifitsradiusincreasesattherateof0.02inchpersecond,howfastistheareaofoneofitsfacesincreasingwhenitsradiusis8.1inches?

____πin.^2/s正确答案：:0.324/1.0181.5homework第1题Bydifferential,theapproximationsto4.1is

____正确答案：:2.025第2题Poiseuille'sLawforbloodflowsaysthatthevolumeflowingthroughanarteryisproportionaltothefourthpoweroftheradius,thatis,V=kR4.Byhowmuchmusttheradiusbeincreasedinordertoincreasethebloodflowby40%?

____正确答案：:10%1.8homework第1题Ineconomics,dRdxiscalled____

,dPdx

iscalled____正确答案：:marginalrevenue正确答案：:marginalprofit第2题Inmanufacturingandsellingxunitsofacertaincommodity,thepricefunctionpandthecostfunctionC(indollars)aregivenbyp(x)=5.00−0.002xC(x)=3.00+1.10xWhenx=____thatwillproducethemaximumtotalprofit.正确答案：:9751.9homework第1题Iffis____

onaclosedinterval[a,b]anddifferentiableon

____,thenthereisatleastonenumbercin(a,b)where

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

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

____ofx=2.Infact,itisat

=____正确答案：:right正确答案：:2.2第2题Thehomogeneousrectangularlaminawithcornerpoints(0,0),(2,0),(2,6)and(0,6)willbalanceat

=____,=____正确答案：:1正确答案：:33.8homework第1题Arandomvariablewhosesetofpossibleoutcomesisfiniteorcanbeputintoaninfinitelistiscalleda

____randomvariable.Arandomvariablewhosesetofpossibleoutcomesmakesupanintervalofrealnumbersiscalleda

____randomvariable.正确答案：:discrete正确答案：:continuous第2题Fordiscreterandomvariables,probabilitiesandexpectationsarefoundbyevaluatinga(an)

____,whereasforcontinuousrandomvariables,probabilitiesandexpectationsarefoundbyevaluatinga(an)

____.正确答案：:sum正确答案：:integral第3题IfacontinuousrandomvariableX

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

∫05f(x)dx第4题Theaccumulationfunction

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

____.

正确答案：:cumulativedistributionfunction3.9homework第1题Ifthenaturallengthofaspringis0.2meter,andifittakesaforceof12Newtonstokeepitextended0.04meter,theworkdoneinstretchingthespringfromitsnaturallengthtoalengthof0.3meteris1.2joules.3.10homework第1题IfaninitialamountofA0dollarsisdepositedinabankpayinganinterestrateofrperyearcompoundedcontinuously,thefuturevalueofthismoneyisgivenbytheformulaFuturevalue

第2题IfoneaimstoobtainanamountofA0

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

3.11homework第1题Ifa1000-poundcapsuleweighsonly165poundsonthemoo