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I would like to know sources, and examples of good "challenge" problems for students who have studied pre-calculus and some calculus. (differentiation and the very basics of integration.) Topics could be related to things such as:

  1. Taylor Series.
  2. Product Rule, Quotient Rule, Chain Rule.
  3. Simple limits.
  4. Delta Epsilon Proofs.
  5. Induction proofs for the sum of the first n, integer, squares, etc.
  6. Integration by substitution.
  7. Other topics...

What I have found so far are too many problems that are just a bit too difficult. The problem can have a "trick" but it needs to be something a freshman could do.

Here is one problem that I thought was just at the right level:

If $f(x) = \frac{x}{x+\frac{x}{x+ \frac{x}{x+ \vdots}}}$, find $f'(x)$*

*To be honest this problem makes me a little nervous. Still, I like it.

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    @a little don: Judging from http://meta.math.stackexchange.com/questions/941/community-wiki-checkbox-disappeared and http://meta.stackexchange.com/questions/67581/community-wiki-checkbox-missing-in-action, one can no longer make a question CW; you need to flag it for moderation. I've done so for this one.2010-11-12
  • 0
    You can read somewhere that the tag can not be a community wiki.2010-11-12

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