2. Re-cap Stay in your assigned seat Be respectful, do not be disruptive. Phones and iPods must be put away Be prepared, do not be lazy. The MHHS Student Behavior Code will be strictly enforced.

3. Winter Break HW 1.Now count how many you completed. 2.Grade your self on correctness. - Come scan your bubble sheet 3.Record your scores. (Correct/Completed)

4. Winter break homework 1. E 3. E 4. D 6. C 7. B 9. A 10. B 13. A 14. E 15. D 16. C 17. A 18. A 20. D 21. A 24. C 25. E 26. B 28. E 76. C 78. C 79. D 80. B 81. D 87. B 89. D 90. B

5. Break downs Score% cutoff 5 ish68% 4 ish51% 3 ish35% 2 ish19% 1Name on paper

6. 5.1 The Area Problem

7. 5.1 The Area Problem How could we approximate the area under the curve?

12. Types of Approximations There are 4 types of approximation methods 3 of them use rectangles, these are the ones we will discuss today. These are called : Riemann sums!

13. RRAM Right-hand rectangle approximation of area method These are called Reimann Sums: These are called Reimann Sums: Click here for a better demonstration. Click here for a better demonstration.

14. LRAM Left-hand rectangle approximation of area method These are called Reimann Sums: These are called Reimann Sums: Click here for a better demonstration. Click here for a better demonstration.

15. MRAM Midpoint rectangle approximation of area method These are called Reimann Sums: These are called Reimann Sums: Click here for a better demonstration. Click here for a better demonstration.

16. Example 1.Use LRAM to approximate the area enclosed by f(x) and the x-axis over the interval [1, 7], using 3 equal subintervals. 2.Now use RRAM to approximate the area enclosed by f(x) and the x-axis over the interval [1, 7]. using 3 equal subintervals. 3.Use MRAM to approximate the area enclosed by f(x) and the x-axis over the interval [1, 7], using 3 equal subintervals.

18. N DA N G! A numerical example 1.Use midpoint Riemann sum with 4 equal subintervals of equal length to approximate the area under the velocity curve of a rocket’s flight. 2.Think about, then discuss what the units might be.

19. ASGN 51 5.1 Worksheet A *WARNING: not all intervals are created equal!