Here's a typical homework assignment I designed for my 2nd semester calculus students at Dalhousie University. In accordance with my Teaching Philosophy, there are several standard problems from the text intended to familiarize students with the concepts.
Question number 4 is a question I designed myself. It is an inversion of the usual "interval of convergence" type of question, where instead of providing the series and asking for the interval, I provide the interval and request a series which has precisely the given interval as the interval of convergence. This type of question is designed to elicit creativity, to get's students thinking about series convergence in new ways, and, by requiring students to construct their own examples, helps them to "own" what they have "learned".
Question number 5 is a popular problem from "recreational" mathematics which students enjoy playing with. Often one can learn the most while engaged in play, but depsite it's "unserious" appearance, there is a hidden connection to the most important divergent series in mathematics.
1. Do §10.9 numbers 6, 14, and 26 on pages 632-633.
2. Do §10.10 numbers 6, 22, 34 and 38 on page 643.
3. Give the 3rd degree Taylor polynomial centred at a=1 for the function f(x)=log x.
4. Give an example of a series with interval of convergence (-1,2].
5. Is it possible to stagger a stack of many calculus textbooks so that the top book would be far out into the room - say 20 or 30 feet?
Due at my office (Chase 304) by noon, Monday, April 13.