1131 Exam 3 Review (13.6-14.10)

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Published on 31 Jan 2019
School
Ohio State University
Department
Mathematics
Course
MATH 1131
Professor
Math1131ReviewforMidterm3(13.614.10)
1. Evaluate
a.
2
1
x
dx
x



 b. 34
5xx
 c. ln( )
x
xe dx
x

d.
12
0
2115
21
xx
dx
x

  e.
2
1
x
edx
x
 f. 32
5
37
x
dx
x



2. Intheproblembelowdr
dq
isamarginalrevenuefunction.Findthedemandfunction.
3
7500 7(2 4 )
dr qq
dq 
3. Findy,subjecttothegivenconditions. 2
327;yxx


(1) 7;y
 (1) 0.y
4. Findanapproximatearea3
Softheregionboundedbythegivencurvesinthefirstquadrant.(Use
therighthandendpointofeachsubinterval.) 2
() ;
f
xx0;y
6x
5. Acompanymanufacturesandsellsxmp3playersperweek.Iftheweeklycostanddemand
equationsaregivenby:( ) 8000 5Cx x
and14 , 0 25,000
4000
x
px
Findtheproductionlevelthatmaximizesprofit.
6. Acompanywishestomanufactureaboxwithavolumeof36cubicfeetthatisopenontopandis
twiceaslongasitiswide.Findthewidthoftheboxthatcanbeproducedusingtheminimum
amountofmaterial.
7. Arealestatefirmowns100apartments.At$400permonth,eachapartmentcanberented.However,for
each$10permonthincrease,therewillbetwovacancieswithnopossibilityoffillingthem.Whatrentper
apartmentwillmaximizethemonthlyrevenue?
8. Amanufacturer’smarginalcostfunctionis2
0.004 0.5 50
dc qq
dq

.Ifcisindollars,determine
thecostinvolvedtoincreaseproductionfrom90to180units.
9. Findtheareaintheregionboundedby3
yx
andyx
.
10. Findtheareaoftheregionboundedby4yx
and22yx
.
11. Findtheareaoftheregionboundedby
y
x,6yx
,andthexaxis.Integrateintermsofx.
12. Thedemandforaproductisgivenby2
500
p
q
anditssupplyisgivenby30 100pq.Find
theconsumers’surplusundermarketequilibrium.
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