DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
k k k k k k k k
Stewart - Calculus 8e Chapter 2 Form A
k k k k k k k
1. Differentiate.
2. Findktheklimit.
3. Differentiate.
4. Thekgraphkshowskthekpercentagekofkhouseholdskinkakcertainkcitykwatchingktelevisionkduringkak24-
hrkperiodkonkakweekdayk(
k correspondsktok6ka.m.).kBykcomputingkthekslopekofkthekrespectivektangentkline,kestimatekthekratekofkchangekofk
thekpercentagekofkhouseholdskwatchingktelevisionkatka-12kp.m.
Notekthatk
0.225
3
dy
0.15
0.075
2k k 4k k 6k k 8 k k 10k 12k 14k 16k 18k 20 tk(hr)
5. SupposekthektotalkcostkinkmaunufacturingkxkunitskofkakcertainkproductkiskCk(x)kdollars.
a. Whatkdoesk k measure? kGivekunits.
b. Whatkcankyouksaykaboutktheksignkofk ?
c. Givenkthatk
k,kestimatekthekadditionalkcostkinkproducingkthek3001stkunitkofkthekproduct.
©k2016kCengagekLearning.kAllkRightskReserved.kMayknotkbekscanned,kcopiedkorkduplicated,korkpostedktokakpubliclykaccessiblekwebsite,kinkwholekorkinkpart.
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, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
k k k k k k k k
Stewart - Calculus 8e Chapter 2 Form A
k k k k k k k
6. TheklevelkofknitrogenkdioxidekpresentkonkakcertainkJunekdaykinkdowntownkMegapoliskiska
pproximatedkby
wherekA(t)kiskmeasuredkinkpollutantkstandardkindexkandktkiskmeasuredkinkhourskwithk
kcorrespondingktok7ka.m.k Whatkiskthekaverageklevelkofknitrogenkdioxidekinkthekatmospherekfromk1
a.m.ktok2kp.m.konkthatkday?k k Roundktokthreekdecimalkplaces.
7. Sketchkthekgraphkofkthekderivativek k ofkthekfunctionk k fk k whosekgraphkiskgiven.
8. Letk .
k
a. Sketchkthekgraphkofk k f.
b. Forkwhatkvalueskofkxkiskfkdifferentiable?
c. Findkakformulakfork .
9. Supposekthatkfkandkgkarekfunctionskthatkarekdifferentiablekatkxk=k1kandkthatkfk(1)k=k1,k (1)k=k–3,kg
(1)k=k2,kandk (1)k=k5.k k Findk .
10. Findkthekderivativekofkthekfunction.
11. Identifykthek“insidekfunction”kuk=kfk(x)kandkthek“outsidekfunction”kyk=kgk(u).k Thenkfindkdy/dxkusingkth
ekChainkRule.
©k2016kCengagekLearning.kAllkRightskReserved.kMayknotkbekscanned,kcopiedkorkduplicated,korkpostedktokakpubliclykaccessiblekwebsite,kinkwholekorkinkpart.
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, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
k k k k k k k k
Stewart - Calculus 8e Chapter 2 Form A
k k k k k k k
12. Findkthekderivativekofkthekfunction.
fk(x)k=kxksin8kx
13. Findkankequationkofkthektangentklinektokthekgivenkcurvekatkthekindicatedkpoint.
14. Thekcurvekwithkthekequation
iskcalledkankasteroid.kFindkankequationkofkthektangentktokthekcurvekatkth
ekpointk(48 6k,k1).
125
–125 0 125k x
–125
©k2016kCengagekLearning.kAllkRightskReserved.kMayknotkbekscanned,kcopiedkorkduplicated,korkpostedktokakpubliclykaccessiblekwebsite,kinkwholekorkinkpart.
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, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
k k k k k k k k
Stewart - Calculus 8e Chapter 2 Form A
k k k k k k k
15. Twokcurveskareksaidktokbekorthogonalkifktheirktangentklineskarekperpendicularkatkeachkpointkofki
ntersectionkofkthekcurves.kShowkthatkthekcurveskofkthekgivenkequationskarekorthogonal.
k7k 7
k
yk–k xk= xk=k cosky
4 4
16. s(t)kiskthekpositionkofkakbodykmovingkalongkakcoordinatekline;ks(t)kiskmeasuredkinkfeetkandktkinksec
onds,kwherek .k k Findkthekposition,kvelocity,kandkspeedkofkthekbodykatkthekindicatedktime.
;
k tk=k3
17. Inkcalmkwaters,kthekoilkspillingkfromkthekrupturedkhullkofkakgroundedktankerkspreadskinkallkdirection
s.k Assumingkthatkthekpollutedkareakiskcircular,kdeterminekhowkfastkthekareakiskincreasing
k1
whenkthekradiuskofkthekcirclekisk20kftkandkiskincreasingkatkthekratekofk ft/sec.k k Roundktoktheknearest
6
tenthkifknecessary.
18. Thekvolumekofkakrightkcircularkconekofkradiuskrkandkheightkhkisk
.k Supposekthatkthekradiuskandkheightkofkthekconekarekchangingkwithkrespectktoktimekt.
a. Findkakrelationshipkbetweenk ,
kk , andk
kk .
k
b. Atkakcertainkinstantkofktime,kthekradiuskandkheightkofkthekconekarek12kin.kandk13kin.kandkarekinc
reasingkatkthekratekofk0.2kin./seckandk0.5kin./sec,krespectively.k Howkfastkiskthekvolumekofkthekc
onekincreasing?
19. Inkcalmkwaters,kthekoilkspillingkfromkthekrupturedkhullkofkakgroundedktankerkspreadskinkallkdirection
s.k Assumingkthatkthekpollutedkareakiskcircular,kdeterminekhowkfastkthekareakiskincreasing
k1
whenkthekradiuskofkthekcirclekisk20kftkandkiskincreasingkatkthekratekofk ft/sec.k k Roundktoktheknearest
6
tenthkifknecessary.
©k2016kCengagekLearning.kAllkRightskReserved.kMayknotkbekscanned,kcopiedkorkduplicated,korkpostedktokakpubliclykaccessiblekwebsite,kinkwholekorkinkpart.
mynursytest.store
k k k k k k k k
Stewart - Calculus 8e Chapter 2 Form A
k k k k k k k
1. Differentiate.
2. Findktheklimit.
3. Differentiate.
4. Thekgraphkshowskthekpercentagekofkhouseholdskinkakcertainkcitykwatchingktelevisionkduringkak24-
hrkperiodkonkakweekdayk(
k correspondsktok6ka.m.).kBykcomputingkthekslopekofkthekrespectivektangentkline,kestimatekthekratekofkchangekofk
thekpercentagekofkhouseholdskwatchingktelevisionkatka-12kp.m.
Notekthatk
0.225
3
dy
0.15
0.075
2k k 4k k 6k k 8 k k 10k 12k 14k 16k 18k 20 tk(hr)
5. SupposekthektotalkcostkinkmaunufacturingkxkunitskofkakcertainkproductkiskCk(x)kdollars.
a. Whatkdoesk k measure? kGivekunits.
b. Whatkcankyouksaykaboutktheksignkofk ?
c. Givenkthatk
k,kestimatekthekadditionalkcostkinkproducingkthek3001stkunitkofkthekproduct.
©k2016kCengagekLearning.kAllkRightskReserved.kMayknotkbekscanned,kcopiedkorkduplicated,korkpostedktokakpubliclykaccessiblekwebsite,kinkwholekorkinkpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
k k k k k k k k
Stewart - Calculus 8e Chapter 2 Form A
k k k k k k k
6. TheklevelkofknitrogenkdioxidekpresentkonkakcertainkJunekdaykinkdowntownkMegapoliskiska
pproximatedkby
wherekA(t)kiskmeasuredkinkpollutantkstandardkindexkandktkiskmeasuredkinkhourskwithk
kcorrespondingktok7ka.m.k Whatkiskthekaverageklevelkofknitrogenkdioxidekinkthekatmospherekfromk1
a.m.ktok2kp.m.konkthatkday?k k Roundktokthreekdecimalkplaces.
7. Sketchkthekgraphkofkthekderivativek k ofkthekfunctionk k fk k whosekgraphkiskgiven.
8. Letk .
k
a. Sketchkthekgraphkofk k f.
b. Forkwhatkvalueskofkxkiskfkdifferentiable?
c. Findkakformulakfork .
9. Supposekthatkfkandkgkarekfunctionskthatkarekdifferentiablekatkxk=k1kandkthatkfk(1)k=k1,k (1)k=k–3,kg
(1)k=k2,kandk (1)k=k5.k k Findk .
10. Findkthekderivativekofkthekfunction.
11. Identifykthek“insidekfunction”kuk=kfk(x)kandkthek“outsidekfunction”kyk=kgk(u).k Thenkfindkdy/dxkusingkth
ekChainkRule.
©k2016kCengagekLearning.kAllkRightskReserved.kMayknotkbekscanned,kcopiedkorkduplicated,korkpostedktokakpubliclykaccessiblekwebsite,kinkwholekorkinkpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
k k k k k k k k
Stewart - Calculus 8e Chapter 2 Form A
k k k k k k k
12. Findkthekderivativekofkthekfunction.
fk(x)k=kxksin8kx
13. Findkankequationkofkthektangentklinektokthekgivenkcurvekatkthekindicatedkpoint.
14. Thekcurvekwithkthekequation
iskcalledkankasteroid.kFindkankequationkofkthektangentktokthekcurvekatkth
ekpointk(48 6k,k1).
125
–125 0 125k x
–125
©k2016kCengagekLearning.kAllkRightskReserved.kMayknotkbekscanned,kcopiedkorkduplicated,korkpostedktokakpubliclykaccessiblekwebsite,kinkwholekorkinkpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
k k k k k k k k
Stewart - Calculus 8e Chapter 2 Form A
k k k k k k k
15. Twokcurveskareksaidktokbekorthogonalkifktheirktangentklineskarekperpendicularkatkeachkpointkofki
ntersectionkofkthekcurves.kShowkthatkthekcurveskofkthekgivenkequationskarekorthogonal.
k7k 7
k
yk–k xk= xk=k cosky
4 4
16. s(t)kiskthekpositionkofkakbodykmovingkalongkakcoordinatekline;ks(t)kiskmeasuredkinkfeetkandktkinksec
onds,kwherek .k k Findkthekposition,kvelocity,kandkspeedkofkthekbodykatkthekindicatedktime.
;
k tk=k3
17. Inkcalmkwaters,kthekoilkspillingkfromkthekrupturedkhullkofkakgroundedktankerkspreadskinkallkdirection
s.k Assumingkthatkthekpollutedkareakiskcircular,kdeterminekhowkfastkthekareakiskincreasing
k1
whenkthekradiuskofkthekcirclekisk20kftkandkiskincreasingkatkthekratekofk ft/sec.k k Roundktoktheknearest
6
tenthkifknecessary.
18. Thekvolumekofkakrightkcircularkconekofkradiuskrkandkheightkhkisk
.k Supposekthatkthekradiuskandkheightkofkthekconekarekchangingkwithkrespectktoktimekt.
a. Findkakrelationshipkbetweenk ,
kk , andk
kk .
k
b. Atkakcertainkinstantkofktime,kthekradiuskandkheightkofkthekconekarek12kin.kandk13kin.kandkarekinc
reasingkatkthekratekofk0.2kin./seckandk0.5kin./sec,krespectively.k Howkfastkiskthekvolumekofkthekc
onekincreasing?
19. Inkcalmkwaters,kthekoilkspillingkfromkthekrupturedkhullkofkakgroundedktankerkspreadskinkallkdirection
s.k Assumingkthatkthekpollutedkareakiskcircular,kdeterminekhowkfastkthekareakiskincreasing
k1
whenkthekradiuskofkthekcirclekisk20kftkandkiskincreasingkatkthekratekofk ft/sec.k k Roundktoktheknearest
6
tenthkifknecessary.
©k2016kCengagekLearning.kAllkRightskReserved.kMayknotkbekscanned,kcopiedkorkduplicated,korkpostedktokakpubliclykaccessiblekwebsite,kinkwholekorkinkpart.
mynursytest.store
