Exam location & times: Olin Hall 103, either 5:30-7:25 or 7:30-9:25, on Tuesday evening, November 14, 2006.

General Rules

• You are allowed one new 3"-by-5" note card with anything you wish written on both sides for use during the exam. You may also use your 3"-by-5" note cards from Exams 1 and 2.
• No other notes or books are allowed at the exam.
• You must have your graphing calculator with you, with angular measure set to radian mode.

• Look over your old homework assignments and in-class exercises.
• Do a few the review problems in the links below and do the "Check Your Understanding" true/false problems.   Answers are posted outside my office. Also look at odd-numbered problems in the Review Exercises and Problems at the end of each chapter.
• Master the ideas given in the document "Testing Series for Convergence"; summarize the information on your note card.
• Think carefully about what else you want to write on your one note card.

Chapter 9: Sequences and Series
• Sequences
• Geometric series
• Convergence of sequences and series
• Tests for convergence
  See list given in class.
• Power series

Chapter 10: Approximating Functions Using Series (excluding Sect. 10.5: Fourier series)
• Taylor polynomials
• Taylor series
• Finding and using Taylor series
• The error in Taylor polynomial approximations

Standard problems
(Be prepared also to think about nonstandard problems.)
• Does a given series converge, i.e., have a "sum"?
• What is the sum--exactly or approximately?
• How many terms of a series must be added to approximate the sum within a given accuracy?
• For which values of x does a given power series converge?
• What is the Taylor polynomial approximation P_n(x) of a given function?
• What is the Taylor series of a given function?
• What is a bound on the error made in using a Taylor polynomial to approximate a given function at a given point or over a given interval?
• What order (degree) of Taylor polynomial approximation should you use to approximate a given function to within a given accuracy?
• Prove that a given function equals its Taylor series (if true).
• Explain what is meant by: infinite series, power series, partial sums, sum of a series, convergence, divergence, Taylor polynomial, Taylor series.
• True/false problems of the "Check Your Understanding" type
• Outline of convergence testing

• Problems on convergence of series (ps) (pdf)
• Solutions of problems on convergence of series (ps) (pdf)
• Power series problems (ps) (pdf)
• Power series solutions (ps) (pdf)
• Taylor polynomials and series:
  10.1: #7, 13, 35; 10.2: #7, 21; 10.3: #5, 15; 10.4: #5, 11; Ch. 10 review: #19, 21
• Answers are in the back of our text.