Exam location & times: Olin Hall 320 at 9:00 a.m. (section 1) or 12:30 p.m. (section 3) on Friday, April 26

General Rules

• You are allowed one new 4"-by-6" 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.
• Be prepared for a two-part exam: The first part is to be done without a calculator. The second part will allow calculator use.

• Look over your old homework assignments and in-class exercises.
• Do a few of the chapters 9 & 10 review problems and "Check Your Understanding" true/false problems.   Answers are posted outside my office.
• For each section of the text that will be covered on the exam, write a paragraph in your own words that describes the main ideas in the section, why these ideas are important, and how you can use the ideas to solve problems.
• Think carefully about what you want to write on your one note card.

Chapter 9: Infinite series
• Geometric series
• Convergence of sequences and series
• Tests for convergence
• Power series
• Plus...
  • Telescoping series
  • Limit comparison test
  • Error bounds for partial sums for alternating series and series that converge by the integral test

Chapter 10: Approximating functions (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

• Chapter 9: 1-16, 21-24
• Chapter 10: 1-6, 9, 12-17, 19, 24, 25ab
• Solutions to the Review Problems are posted outside Olin 307.
• 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)