Find the error!

This is a website that is used by teachers as a fun way of giving some extra credit/challenge to their students. The solutions are not up on the website for a reason. If a student wants to email me, to help if they are stuck, I'm usually friendly about that. But if a student asks you to provide them with an answer, then you are helping them cheat, and I would ask that you politely decline.

I wrote most of the following problems for the Instructor's Guide for Stewart's Calculus, Concepts and Contexts, ISBN 0-534-390447. They all consist of a "proof", using calculus, that leads to a contradiction, such as 1 = 0, or that sin(x) is always positive. The student's job is to go through the proof, figure out the error, and thus confront common misconceptions about the concepts of calculus.

I have used these as extra-credit problems, and my students have quite enjoyed puzzling over them. They also may be used as a final project in an AP class, assigned between the AP test and the end of the semester. Please let me know if you use them, and if you and your students found them worthwhile.

1)	Find the error: Differentiation
2)	Find the error: Fundamental Theorem of Calculus
3)	Find the error: U-substitution
4)	Find the error: Trigonometric Integration
5)	Find the error: Integration by Parts (part 1)
6)	Find the error: Integration by Parts (part 2)
7)	Find the error: L'Hopital's Rule
8)	Find the error: Related Rates
9)	Find the error: Separation of Variables
10)	Find the error: Separation of Variables - Exponential Growth
11)	Find the error: Improper Integrals and Taylor Series
	Find the error: Solutions Find the error: Credits

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