Message from Professor Bozenna Pasik-Duncan: 10/30/13
Dear Students,
Reviewing the following sections with illustrative examples will help you to be well-prepared for Exam II on Wednesday, November 6, 5:45 pm - 7:45 pm.
- Chapter 4:
- 4.2: Maximum and Minimum Values – Examples: 1, 2, 3, 4, 5, 6, 7
- 4.3: Derivatives and the Shapes of Curves – Examples: 2, 3, 4, 5, 6
- 4.6: Optimization Problems – Examples: 1, 2, 3, 5, 6
- 4.8: Antiderivatives – Examples: 1, 2, 3, 4, 5, 6
- Chapter 5:
- 5.1: Areas – Examples: 1
- 5.2: The Definite Integral – Examples: 1, 2, 4, 5, 6, 7
- 5.3: Evaluating Definite Integral – Examples: 1, 2, 3, 6
- 5.4: The Fundamental Theorem of Calculus – Examples: 2, 3, 5
- 5.5: The Substitution Rule – Examples: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- Chapter 6:
- 6.1: Area Between Curves – Examples: 1, 2
- 6.5: The Average Value of a Function – Examples: 1
The exam will focus on the following concepts:
1. Monotonicity and Extrema (local and absolute).
2. Concavity and Points of infection.
3. Limits and Asymptotes.
4. Analysis of Functions.
5. Optimization Problems including optimization of average cost, revenue, profit.
6. Integration Techniques including power rule, exponential and logarithmic functions, substitution method, approximation methods.
7. Applications of Integrals including finding areas under a curve and between curves (Sec. 6.1 – integrating with respect to x only), recovering a position function from given acceleration, from marginal cost, marginal profit, marginal revenue, the average value of a given function (Sec. 6.5).
The Extra Credit Problem will focus on choosing one of the following applications of integrals:
1. Numerical Approximation of an integral by using the sum of areas of rectangles.
2. The area between given curves (Section 6.1 – integrating with respect to x only).
3. The average value of a given function (Section 6.5).
To further prepare for the exam, you should study lecture/lab notes and HW problems from the above-listed sections, attend all lecture/lab meetings, and participate in the Special Evening Review Session on Tuesday, November 5 (from 5:45 - 7:45 p.m. in 120 Budig Hall).
Each student may prepare one (double-sided) 3"x5" note card for use during Exam 2!
Good Luck with your preparation! Work very hard!
With my best wishes to each and everyone,
Bozenna Pasik-Duncan