Math 222-06 (Calculus II) Announcements

Corrections and Additions to the Textbook

• Section 12.1, Theorem 6 on limits (page 715): If lim |a_n| = 0, then lim a_n = 0. This is very useful and you should keep it in mind when doing limits. It's especially helpful when applying the Test for Divergence to series whose terms are not necessarily positive.
  
  
• Section 12.4, the Limit Comparison Test (page 743): There are two more parts which the book has only in the exercises, but which you should feel free to use whenever they help (which is pretty often). Supppose Σ a_n and Σ b_n are series with positive terms.
  1. If lim a_n/b_n = 0, and if Σ b_n (the bigger series) converges, then Σ a_n converges also.
  2. If lim a_n/b_n = infinity, and if Σ a_n (the smaller series) diverges, then Σ b_n diverges also.
• Section 12.9, #36 (page 770): There is an error in the second part of the problem. x = 2nπ should be x = 2kπ, k an integer.
• Section 12.11, ##3-10 (page 791): The problem set asks for T_n(x), but it must mean to ask for T₃(x). (There is no reasonable way we can calculate all T_n(x).)