Find the Error: Credits

The actual text of all the problems is my own, the wild-eyed stranger being based on a character from my past.


My friend, Ed Ting, showed this to me during our Freshman year of college. It was not his original creation, but I have never seen it in print, making it true oral tradition math-folklore.

L’Hopital’s Rule

This is original. I was explaining L’Hopital’s rule to a student when I made this error.

Related Rates

This error is discovered by at least three students every time I teach Related Rates. They tend to discover the error while taking exams.

Fundamental Theorem of Calculus

This is original, based on a conversation I had with Paul Froeschl.


Mike Lawler wrote this on my blackboard one Fall afternoon. I’m not sure if he came up with it, or had seen it somewhere.

Integration by Parts (part 1)

This is original. When I was an engineer at GE, another engineer asked me to explain integration by parts to him. We used tan(x) as an example, because we knew how to do it another way, so we could check our work. At the end, the 0 = -1 stood there, glaring at us like an angered cat. Under the pressure, I couldn’t find my mistake, and just had to assure my colleague that integration by parts DOES work. For all I know, the submarine division of GE might STILL refuse to look at the technique with anything but suspicion.

Integration by Parts (part 2)

After I had figured out my error, the natural thing to consider was, “What about definite integrals, where there are no constants?” And I made mistake number two.

Trigonometric Integration

This came from Harvey Keynes and/or Bob Hesse. Probably Bob.

Taylor Series

Russ Campbell gave an old calculus book to me – very old – and I don’t remember the name of it or its author. But this problem was in there, and now it is in here!

Improper Integrals and Taylor Series

Another original one, based on a common misconceptions students have about Taylor Polynomials.

Separation of Variables

Jerry Uhl posted this one on the AP Calculus mailing list. It is public domain.

Separation of Variables – Exponential Growth

I based this on a problem Andy Poe sent to me. Andy has since told me that he based HIS on a problem I made up in graduate school. So this one comes from my younger, smarter self via Andy Poe.

  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