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 for help if they are stuck, I’m usually friendly about that. But if you post solutions online then you are helping them cheat, and I would ask that you do not do so.

I believe that a great deal of learning happens when we try to “debug” someone else’s work. It’s one of the reasons there is truth in the cliche “You don’t really know a subject until you teach it.” These problems all consist of a “proof”, using calculus, that leads to a contradiction, such as 0 = 1. 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. I wrote most of them for the Instructor’s Guide for Stewart’s Calculus, Concepts and Contexts, and there are also some pre-calculus ones in the Instructor’s Guide for Stewart’s Pre-calculus.

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