Saturday, October 15, 2005

Some book questions to help prepare for midterm #1

We had homework on sections 11.1,2,3,4,6,8,9,10.
We discussed some of the material from 11.5 (alternating series) and 11.7 (strategies for testing for convergence) in class; you should know these too.
11.11, 11.12 you can ignore (for now, at least).

Sequences aren't as important for us as series, especially power series, so pay more attention to the later sections.

Basically, you should be able to do any question in 11.7, and at least one of these will be on the test.

The questions 11.8 #3-28 are another good group to be comfortable with.
#29 is tricky and you should be able to do it. The only way to answer a "If you know A, does it follow that B?" question with "No" is to say "No; here's a series for which A is true, but B is not true." If all you say is "I don't see how to get B from A" you leave open the possibility that someone else might. This is one reason it's worth memorizing examples of weird behavior.

11.9 #9,10,15-18,38. (This last one's a little more work than you'll actually see on the test.)
11.10 #3-18. For Taylor series centered at a different from 0, you evaluate derivatives at a instead of 0. Know your sin from your cos!
#23-32 are good too; you should be able to plug in, multiply, differentiate.

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