MAC 2312

Review Sheet, Exam 3

December 1, 2008

When: December 8, 3:00-4:50

What Material: Chapter 9, excluding 9.8

Procedure: The test will be closed book.  You will have the entire class period for the test.  One page (8 1/2 by 11 in, front and back) of notes will be allowed.

Thoughts:  I won't be telling you which test to use to tell if a series converges or diverges, so you will have to figure that out yourself.  Practice with homework sets that don't tell you which test to use.  If you read this, draw a smiley face on the front of your test.  It will make me happy.  If you are a flash card type of person, write down different series from each section on flash cards, shuffle, and then try to do them.  Use the methods talked about in class and covered on page 644 to determine which test is right for you.

New Material:

• Sequences.  Eh, easy.  Well, ok, relatively easy.  Don't expect too many problems that specifically ask you to find the limit of a sequence.  Still, make sure you can (since you need them for lots of series tests), make sure you don't get them confused with series, and make sure you know the how to use dominance to find a limit.  Practice Problems: 9.1, 37-42, 47-68.
• Geometric Series.  You can find the exact sums of them.  That makes them good test fodder.  Practice Problems: 9.2, 31-34, 39-48, 51-56.
• Telescoping Series. They may be useless, but you do have the ability to sum them up.  I might throw one on the exam.  Practice Problems: 9.2, 29, 30, 35-38.
  
• Convergence Tests:  Yup, lots of these.  Make sure you know them all, and you can tell which one to use just by looking at a problem.  Practice Problems: 9.2, 57-72; 9.3, 1-20, 29-36; 9.4, 3-36 (29-36 especially); 9.6, 13-32, 37-68 (51-68 especially).
  
• Alternating Series:  The test is easy, but these have the alternating error estimate.  You need to worry about both.  Practice Problems: 9.5, 11-46, 79-88.
  
• Taylor and Maclaurin Polynomials: As far as you are concerned, this is just a big, ugly formula.  Make sure you can do this big, ugly formula.  Also, you should understand what these polynomials are. Practice Problems: 9.7, 13-30.
  
• Taylor and Maclaurin Series:  Be able to derive series from ones you already know, and be able to determine the first couple of terms of a Taylor series using the ugly formula.  Also expect to approximate some numbers using these series combined with the alternating remainder theorem.  Practice Problems: 9.9, 1-26, 35-38; 9.10, 1-10, 21-29, 31-34, 49-52, 55-58, 61, 62.
  
• Taylor Series to Know: You should know (i.e., have on your cheat sheet), the series for 1/(1-x), 1/(1+x), e^x, sin(x), cos(x), and arctan(x).  You can then use these series to make new series for changed functions (like e^3x, sin(x²), etc).