Chapter 8.1 Puzzle

### This assignment is due 48 hours after the Chapter Test is given.

• Puzzle solutions are due by 5:00 PM two days after the Chapter Test.
• Puzzles are worth 10 points of extra credit each.
• Answers must be accompanied by valid reasoning. Just like the tests, the answer alone isn't enough!

"Find the Error"

It is a beautiful day. You leave your calculus class feeling sad and depressed. You aren't sad because of the class itself. On the contrary, you have the finest mathematics professor around and you just learned an amazing integration technique: Integration by Parts. You aren't sad because it is your birthday. On the contrary, you are still young enough to actually be happy about it. You are sad because you know that every time you learn something really wonderful in calculus, a wild-eyed stranger runs up to you and shows you a "proof" that is false. Sure enough, as you cross the Michigan Street, he is waiting on the other side.

"Good morning, Sonny," he says.

"I just learned integration by parts. Let me have it."

"What do you mean?" he asks.

"Aren't you going to run around telling me that all of math is lies?"

"Well, if you insist," he chuckles and hands you a piece of paper:

"Hey," you say, "I don't get it! You did everything right!"

"Yup!" says the hungry looking stranger.

"But ... zero isn't equal to negative one!"

Find the error in the wild-eyed stranger's reasoning.