1. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 1 Bruce Mayer, PE Mathematics 16: Applied Calculus-II Bruce Mayer, PE Licensed Electrical & Mechanical Engineer BMayer@ChabotCollege.edu MTH 16 MidTerm Exam-1 Review

2. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 2 Bruce Mayer, PE Mathematics 16: Applied Calculus-II 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. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 3 Bruce Mayer, PE Mathematics 16: Applied Calculus-II Improper Integral  Determine the Value (a number) of J as defined by the Improper Integral Below

4. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 4 Bruce Mayer, PE Mathematics 16: Applied Calculus-II

5. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 5 Bruce Mayer, PE Mathematics 16: Applied Calculus-II

6. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 6 Bruce Mayer, PE Mathematics 16: Applied Calculus-II 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. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 7 Bruce Mayer, PE Mathematics 16: Applied Calculus-II Adding Integrals

8. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 8 Bruce Mayer, PE Mathematics 16: Applied Calculus-II Adding Integrals

9. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 9 Bruce Mayer, PE Mathematics 16: Applied Calculus-II 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

10. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 10 Bruce Mayer, PE Mathematics 16: Applied Calculus-II 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

11. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 11 Bruce Mayer, PE Mathematics 16: Applied Calculus-II

12. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 12 Bruce Mayer, PE Mathematics 16: Applied Calculus-II

13. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 13 Bruce Mayer, PE Mathematics 16: Applied Calculus-II

14. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 14 Bruce Mayer, PE Mathematics 16: Applied Calculus-II 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. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 15 Bruce Mayer, PE Mathematics 16: Applied Calculus-II 2 nd Partials Test  FIND For This Function Relative Max or Min Saddle Points

16. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 16 Bruce Mayer, PE Mathematics 16: Applied Calculus-II

17. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 17 Bruce Mayer, PE Mathematics 16: Applied Calculus-II

18. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 18 Bruce Mayer, PE Mathematics 16: Applied Calculus-II

19. BMayer@ChabotCollege.edu MTH16_MTE1_Review.pptx 19 Bruce Mayer, PE Mathematics 16: Applied Calculus-II 2 nd Partials Test  See Also MuPAD File: 3D_Plot_Max_Min_MTE1_Review_BM ayer_1402.mn