DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
n n n n n n n n
Stewart - Calculus 8e Chapter 2 Form A
n n n n n n n
1. Differentiate.
2. Findnthenlimit.
3. Differentiate.
4. Thengraphnshowsnthenpercentagenofnhouseholdsninnancertainncitynwatchingntelevisionnduringnan24-
hrnperiodnonnanweekdayn(
n correspondsnton6na.m.).nByncomputingnthenslopenofnthenrespectiventangentnline,nestimatenthenratenofnchangenofn
thenpercentagenofnhouseholdsnwatchingntelevisionnatna-12np.m.
Notenthatn
0.225
3
dy
0.15
0.075
2n n 4n n 6n n 8n n 10n 12n 14n 16n 18n 20 tn (hr)
5. SupposenthentotalncostninnmaunufacturingnxnunitsnofnancertainnproductnisnCn(x)ndollars.
a. Whatndoesn n measure?nGivenunits.
b. Whatncannyounsaynaboutnthensignnofn ?
c. Givennthatn
n,nestimatenthenadditionalncostninnproducingnthen3001stnunitnofnthenproduct.
©n2016nCengagenLearning.nAllnRightsnReserved.nMaynnotnbenscanned,ncopiednornduplicated,nornpostedntonanpubliclynaccessiblenwebsite,ninnwholenorninnpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
n n n n n n n n
Stewart - Calculus 8e Chapter 2 Form A
n n n n n n n
6. ThenlevelnofnnitrogenndioxidenpresentnonnancertainnJunendayninndowntownnMegapolisnisna
pproximatednby
wherenA(t)nisnmeasuredninnpollutantnstandardnindexnandntnisnmeasuredninnhoursnwithn
ncorrespondingnton7na.m.n Whatnisnthenaveragenlevelnofnnitrogenndioxideninnthenatmospherenfromn1
a.m.nton2np.m.nonnthatnday?n n Roundntonthreendecimalnplaces.
7. Sketchnthengraphnofnthenderivativen n ofnthenfunctionn n fn n whosengraphnisngiven.
8. Letn .
n
a. Sketchnthengraphnofn n f.
b. Fornwhatnvaluesnofnxnisnfndifferentiable?
c. Findnanformulanforn .
9. Supposenthatnfnandngnarenfunctionsnthatnarendifferentiablenatnxn=n1nandnthatnfn(1)n=n1,n (1)n=n–3,ng
(1)n=n2,nandn (1)n=n5.n n Findn .
10. Findnthenderivativenofnthenfunction.
11. Identifynthen“insidenfunction”nun=nfn(x)nandnthen“outsidenfunction”nyn=ngn(u).n Thennfindndy/dxnusingnth
enChainnRule.
©n2016nCengagenLearning.nAllnRightsnReserved.nMaynnotnbenscanned,ncopiednornduplicated,nornpostedntonanpubliclynaccessiblenwebsite,ninnwholenorninnpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
n n n n n n n n
Stewart - Calculus 8e Chapter 2 Form A
n n n n n n n
12. Findnthenderivativenofnthenfunction.
fn(x)n=nxnsin8nx
13. Findnannequationnofnthentangentnlinentonthengivenncurvenatnthenindicatednpoint.
14. Thencurvenwithnthenequation
isncallednannasteroid.nFindnannequationnofnthentangentntonthencurvenatnth
enpointn(48 6n,n1).
125
–125 0 125n x
–125
©n2016nCengagenLearning.nAllnRightsnReserved.nMaynnotnbenscanned,ncopiednornduplicated,nornpostedntonanpubliclynaccessiblenwebsite,ninnwholenorninnpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
n n n n n n n n
Stewart - Calculus 8e Chapter 2 Form A
n n n n n n n
15. Twoncurvesnarensaidntonbenorthogonalnifntheirntangentnlinesnarenperpendicularnatneachnpointnofni
ntersectionnofnthencurves.nShownthatnthencurvesnofnthengivennequationsnarenorthogonal.
n7n 7
n
yn–n xn= xn=n cosny
4 4
16. s(t)nisnthenpositionnofnanbodynmovingnalongnancoordinatenline;ns(t)nisnmeasuredninnfeetnandntninnsec
onds,nwheren .n n Findnthenposition,nvelocity,nandnspeednofnthenbodynatnthenindicatedntime.
;
n tn=n3
17. Inncalmnwaters,nthenoilnspillingnfromnthenrupturednhullnofnangroundedntankernspreadsninnallndirection
s.n Assumingnthatnthenpollutednareanisncircular,ndeterminenhownfastnthenareanisnincreasing
n1
whennthenradiusnofnthencirclenisn20nftnandnisnincreasingnatnthenratenofn ft/sec.n n Roundntonthennearest
6
tenthnifnnecessary.
18. Thenvolumenofnanrightncircularnconenofnradiusnrnandnheightnhnisn
.n Supposenthatnthenradiusnandnheightnofnthenconenarenchangingnwithnrespectntontiment.
a. Findnanrelationshipnbetweenn ,
nn , andn
nn .
n
b. Atnancertainninstantnofntime,nthenradiusnandnheightnofnthenconenaren12nin.nandn13nin.nandnareninc
reasingnatnthenratenofn0.2nin./secnandn0.5nin./sec,nrespectively.n Hownfastnisnthenvolumenofnthenc
onenincreasing?
19. Inncalmnwaters,nthenoilnspillingnfromnthenrupturednhullnofnangroundedntankernspreadsninnallndirection
s.n Assumingnthatnthenpollutednareanisncircular,ndeterminenhownfastnthenareanisnincreasing
n1
whennthenradiusnofnthencirclenisn20nftnandnisnincreasingnatnthenratenofn ft/sec.n n Roundntonthennearest
6
tenthnifnnecessary.
©n2016nCengagenLearning.nAllnRightsnReserved.nMaynnotnbenscanned,ncopiednornduplicated,nornpostedntonanpubliclynaccessiblenwebsite,ninnwholenorninnpart.
mynursytest.store
n n n n n n n n
Stewart - Calculus 8e Chapter 2 Form A
n n n n n n n
1. Differentiate.
2. Findnthenlimit.
3. Differentiate.
4. Thengraphnshowsnthenpercentagenofnhouseholdsninnancertainncitynwatchingntelevisionnduringnan24-
hrnperiodnonnanweekdayn(
n correspondsnton6na.m.).nByncomputingnthenslopenofnthenrespectiventangentnline,nestimatenthenratenofnchangenofn
thenpercentagenofnhouseholdsnwatchingntelevisionnatna-12np.m.
Notenthatn
0.225
3
dy
0.15
0.075
2n n 4n n 6n n 8n n 10n 12n 14n 16n 18n 20 tn (hr)
5. SupposenthentotalncostninnmaunufacturingnxnunitsnofnancertainnproductnisnCn(x)ndollars.
a. Whatndoesn n measure?nGivenunits.
b. Whatncannyounsaynaboutnthensignnofn ?
c. Givennthatn
n,nestimatenthenadditionalncostninnproducingnthen3001stnunitnofnthenproduct.
©n2016nCengagenLearning.nAllnRightsnReserved.nMaynnotnbenscanned,ncopiednornduplicated,nornpostedntonanpubliclynaccessiblenwebsite,ninnwholenorninnpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
n n n n n n n n
Stewart - Calculus 8e Chapter 2 Form A
n n n n n n n
6. ThenlevelnofnnitrogenndioxidenpresentnonnancertainnJunendayninndowntownnMegapolisnisna
pproximatednby
wherenA(t)nisnmeasuredninnpollutantnstandardnindexnandntnisnmeasuredninnhoursnwithn
ncorrespondingnton7na.m.n Whatnisnthenaveragenlevelnofnnitrogenndioxideninnthenatmospherenfromn1
a.m.nton2np.m.nonnthatnday?n n Roundntonthreendecimalnplaces.
7. Sketchnthengraphnofnthenderivativen n ofnthenfunctionn n fn n whosengraphnisngiven.
8. Letn .
n
a. Sketchnthengraphnofn n f.
b. Fornwhatnvaluesnofnxnisnfndifferentiable?
c. Findnanformulanforn .
9. Supposenthatnfnandngnarenfunctionsnthatnarendifferentiablenatnxn=n1nandnthatnfn(1)n=n1,n (1)n=n–3,ng
(1)n=n2,nandn (1)n=n5.n n Findn .
10. Findnthenderivativenofnthenfunction.
11. Identifynthen“insidenfunction”nun=nfn(x)nandnthen“outsidenfunction”nyn=ngn(u).n Thennfindndy/dxnusingnth
enChainnRule.
©n2016nCengagenLearning.nAllnRightsnReserved.nMaynnotnbenscanned,ncopiednornduplicated,nornpostedntonanpubliclynaccessiblenwebsite,ninnwholenorninnpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
n n n n n n n n
Stewart - Calculus 8e Chapter 2 Form A
n n n n n n n
12. Findnthenderivativenofnthenfunction.
fn(x)n=nxnsin8nx
13. Findnannequationnofnthentangentnlinentonthengivenncurvenatnthenindicatednpoint.
14. Thencurvenwithnthenequation
isncallednannasteroid.nFindnannequationnofnthentangentntonthencurvenatnth
enpointn(48 6n,n1).
125
–125 0 125n x
–125
©n2016nCengagenLearning.nAllnRightsnReserved.nMaynnotnbenscanned,ncopiednornduplicated,nornpostedntonanpubliclynaccessiblenwebsite,ninnwholenorninnpart.
mynursytest.store
, DOWNLOAD THE Test Bank for Calculus 8th Edition Stewart
n n n n n n n n
Stewart - Calculus 8e Chapter 2 Form A
n n n n n n n
15. Twoncurvesnarensaidntonbenorthogonalnifntheirntangentnlinesnarenperpendicularnatneachnpointnofni
ntersectionnofnthencurves.nShownthatnthencurvesnofnthengivennequationsnarenorthogonal.
n7n 7
n
yn–n xn= xn=n cosny
4 4
16. s(t)nisnthenpositionnofnanbodynmovingnalongnancoordinatenline;ns(t)nisnmeasuredninnfeetnandntninnsec
onds,nwheren .n n Findnthenposition,nvelocity,nandnspeednofnthenbodynatnthenindicatedntime.
;
n tn=n3
17. Inncalmnwaters,nthenoilnspillingnfromnthenrupturednhullnofnangroundedntankernspreadsninnallndirection
s.n Assumingnthatnthenpollutednareanisncircular,ndeterminenhownfastnthenareanisnincreasing
n1
whennthenradiusnofnthencirclenisn20nftnandnisnincreasingnatnthenratenofn ft/sec.n n Roundntonthennearest
6
tenthnifnnecessary.
18. Thenvolumenofnanrightncircularnconenofnradiusnrnandnheightnhnisn
.n Supposenthatnthenradiusnandnheightnofnthenconenarenchangingnwithnrespectntontiment.
a. Findnanrelationshipnbetweenn ,
nn , andn
nn .
n
b. Atnancertainninstantnofntime,nthenradiusnandnheightnofnthenconenaren12nin.nandn13nin.nandnareninc
reasingnatnthenratenofn0.2nin./secnandn0.5nin./sec,nrespectively.n Hownfastnisnthenvolumenofnthenc
onenincreasing?
19. Inncalmnwaters,nthenoilnspillingnfromnthenrupturednhullnofnangroundedntankernspreadsninnallndirection
s.n Assumingnthatnthenpollutednareanisncircular,ndeterminenhownfastnthenareanisnincreasing
n1
whennthenradiusnofnthencirclenisn20nftnandnisnincreasingnatnthenratenofn ft/sec.n n Roundntonthennearest
6
tenthnifnnecessary.
©n2016nCengagenLearning.nAllnRightsnReserved.nMaynnotnbenscanned,ncopiednornduplicated,nornpostedntonanpubliclynaccessiblenwebsite,ninnwholenorninnpart.
mynursytest.store
