MidTerm Exam-1 Review MTH 16
MTH 16
MidTerm
Exam-1
Review
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Student Reference Card
Student Reference CARD =
A 3"x5" Flash-Card upon which the student may write
ANYTHING that he/she thinks might help him/her do better on the MidTerm Exam
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Improper Integral
Determine the Value (a number) of J as defined by the Improper Integral Below
𝐽 =
2
∞ 7
𝑧 2 +2𝑧+1 𝑧 2 +2𝑧−8 𝑑𝑧 =
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
IJ = 7/((z^2+2*z+1)*sqrt(z^2+2*z-
8))
JJ:=int(7/((z^2+2*z+1)*sqrt(z^2+2* z-8)),z)
J:=int(7/((z^2+2*z+1)*sqrt(z^2+2*z
-8)), z=2..infinity)
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Adding Integrals
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Adding Integrals
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Cobb-Douglas Model
The Cobb-Douglas Model for
P the Chabot Motor Company
L , K
0 .
532 L
0 .
456
K
0 .
544
• Where
– P ≡ Vehicle Production in k-
Vehicles per Year
– L ≡ Labor Costs in $M/year
– K ≡ Capital Costs in $M/year
In Calendar Year 2013 CMC
• Produced 7525 k-Vehicles
• Spent $25 800M on Labor
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Cobb-Douglas Model
CMC plans to Increase
Production by 1% in 2014
• If there is NO additional
Capital, How much added
Labor, ΔL , is required?
• If there is NO additional Labor,
How much added Capital, ΔK , is required?
Chabot Motor Company
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Chabot Motor Co.
P := 7525; a := 0.532; L := 25800; u := 0.456; v := 0.544;
K := (P/(a*L^u))^(1/v) dPdL := a*K^v*u*L^(u-1) dPdK := a*L^u*v*K^(v-1)
DL := 0.01*P/dPdL
DK := 0.01*P/dPdK
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
2
nd
Partials Test
FIND For This Function
• Relative Max or Min
• Saddle Points
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
Mathematics 16: Applied Calculus-II
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
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Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
2
nd
Partials Test
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See Also MuPAD File:
3D_Plot_Max_Min_MTE1_Review_BM ayer_1402.mn
Mathematics 16: Applied Calculus-II Bruce Mayer, PE
BMayer@ChabotCollege.edu • MTH16_MTE1_Review.pptx
