I'm going to talk with someone at a local university tomorrow to see if I can get out of AP Calculus. Essentially, I would like to be prepared for our meeting tomorrow. I'm good with integrals, so that shouldn't be a problem. However, I'm not quite as confident with derivatives, limits, and sums. I'm aware of a similar thread for integrals, but upon cursory inspection there isn't a corresponding thread for these three. I would therefore like to ask the community here for some challenging problems for summations, limits, and derivatives, so I can prove to myself that I'm prepared. Guidelines for problems: I'm not partial to any specific "year" of calculus (and I don't make that distinction very well anyway), so any given difficulty level is fine. I'm looking mostly for calculation-type problems, but I like proofs too. I'm mainly looking for something to convince me I'll do fine on any problem he'll give me tomorrow.