The final exam is CUMULATIVE, that is, it covers all the material from the first day of class onwards. Approximately 15 - 20% will cover material from Chapter 8 on Infinite Sequences and Series. This is Sections 8.1 - 8.5.

It is recommended that you go over homework problems, quizzes, the midterm exams and your class notes. Many of the problems and questions we discuss in class are excellent examples of test questions. The solutions to your WebAssign problems can be seen by clicking "View Key" near the top of each assignment. You can click ``Practice Another Version'' after each problem to try the same problem but with different numbers.

I have listed some sample problems from the Chapter 8 Review below. The odd answers are in the back of the book while the evens are listed here. For questions from other chapters, see the previous exam review sheets: Exam 1 (Chapters 1, 2, 3.1 - 3.7) , Exam 2 (Chapters 3.8, 3.9, 4, 5.1 - 5.7) , Exam 3 (Chapters 5.8 - 5.10, 6, 7.1 - 7.4) Note that some sections are poorly covered by the problems in the Chapter Review Exercises (eg. trig. substitution is missing in Ch. 5.) The Concept-Check and True-False Quiz at the end of each chapter (before the exercises) are also a good source for questions.

The exam will be designed to take 1.5 - 2 hours although you will have the full 2.5 hours to complete the exam. Click here for a sample final exam (PDF File). Click here for solutions to the sample final.

**Note:** You will be allowed one "cheat sheet" 8.5 x 11 piece of paper, front and back,
full of whatever formulas, graphs, etc. you wish. You will be given a
scientific calculator for the exam which does NOT have graphing
capabilities so be prepared to answer questions without your personal
calculator or computer. The only numerical computations required will be the kind
a scientific calculator can perform.

**Exam Review:** We will review for the exam Monday, Dec. 13, 1:00 - 2:30 pm
in Swords 302. Please come prepared with specific questions.

**Chapter 8 Review Exercises, pp. 629 - 630**

Problems: 1, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 21, 31, 32, 33

The answers to the evens are:

4. Diverges (cycles through the values 0, 1, 0, -1, ...)

10. Diverges by the Comparison Test (compare to harmonic series)

12. Converges by the Alternating Series Test

14. Diverges by the n-th Term Test

16. Converges by the Comparison Test (compare with a geometric series after taking absolute value)

18. Diverges by the Ratio Test

32. Converges for all real numbers, radius of convergence = infinity.