1. Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu
MTH 16
MidTerm Exam-1 Review
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer

2. 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

3. Improper Integral
Determine the Value (a number) of J as defined by the Improper Integral Below

6. JJ:=int(7/((z^2+2*z+1)*sqrt(z^2+2*z-8)),z)
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)

7. Adding Integrals

8. Adding Integrals

9. 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 2016 CMC
Produced 7525 k-Vehicles
Spent $25 800M on Labor

10. Cobb-Douglas Model Chabot Motor Company
CMC plans to Increase Production by 1% in 2017
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

13. 1% INCREASE EITHER:

14. 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

15. 2nd Partials Test FIND For This Function Relative Max or Min
Saddle Points
3D_Plot_Max_Min_MTE1_Review_BMayer_1402.mn

17. OVER COMMON DENOM

18. OVER COMMON DENOM

19. 2nd Partials Test
See Also MuPAD File: 3D_Plot_Max_Min_MTE1_Review_BMayer_1402.mn