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|
the error: Fundamental Theorem of Calculus|
|3)||Find the error: U-substitution|
the error: Trigonometric Integration|
the error: Integration by Parts (part 1)|
the error: Integration by Parts (part 2)|
the error: L'Hopital's Rule|
the error: Related Rates|
the error: Separation of Variables|
|10)||Find the error: Separation of Variables
- Exponential Growth|
the error: Improper Integrals and Taylor Series|
Find the error: Solutions
Find the error: Credits
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Copyright 2001 by Douglas Shaw