Find the error! Credits!

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

1) Find the error: Differentiation

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.

2) Find the error: Fundamental Theorem of Calculus

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

3) Find the error: U-substitution

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.

4) Find the error: Trigonometric Integration

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

5) Find the error: Integration by Parts (part 1)

This was 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 refuses to look at the technique with anything but suspicion.

6) Find the error: 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?"

7) Find the error: L'Hopital's Rule

Another original one. I was explaining L'Hopital's rule to a student when I made this error.

8) Find the 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.

9) Find the error: Separation of Variables

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

10) Find the error: 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.

11) Find the error: Improper Integrals and Taylor Series Find the error: Solutions

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

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