Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

[email protected] • MTH16_MTE1_Review.pptx1

Bruce Mayer, PE Mathematics 16: Applied Calculus-II

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

MTH 16

MidTerm

Exam-1Review



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



Improper Integral

Determine the Value (a number) of J as defined by the Improper Integral Below𝐽= 7

ሺ𝑧2+2𝑧+1ሻξ𝑧2+2𝑧−8𝑑𝑧∞2 =







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)



Adding Integrals



Adding Integrals



Cobb-Douglas Model

The Cobb-Douglas Model for the Chabot Motor Company

• 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

544.0456.0532.0, KLKLP



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

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=BbVhAnCZTRZYOM&tbnid=qTyzNEIN1yCOJM:&ved=0CAUQjRw&url=http://www.taxisedona.com/about-us/&ei=p8T3UtSJCozhoAS9_IHgCA&bvm=bv.60983673,d.cGU&psig=AFQjCNHoObo3d87_XUFZawgjOCxKYnRi_A&ust=1392055801209301









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



2nd Partials Test

FIND For This Function

• Relative Max or Min• Saddle Points









2nd Partials Test

See Also MuPAD File:3D_Plot_Max_Min_MTE1_Review_BMayer_1402.mn

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege

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added capital