Vito Prosciutto: Teaching community college math on the road to a PhD.

Tuesday, September 28, 2004

Mean Girls 

[warning some heavy math content appears below] Kevin Drum at The Washington Monthly mentioned the movie Mean Girls today, and I have to say that the scene that he mentioned thrilled me too (not to mention that it's nice to see a movie in which the cool teacher is the math teacher). He mentions this problem which appears at the climax of the film:

I have to admit that when the question came up on the screen when I was watching the movie, I was trying to solve the problem.

What's distressing is how many of the commenters on this post got the math wrong.

As a math geek, I see a limit of a rational expression, and my first thought is L'Hopital's rule. Since the numerator and denominator are both 0 at x=0, we can find the limit by taking the derivative of the numerator and denominator. Lot's of important special derivatives to employ, plus the chain rule. Where some people go wrong is that when they get to this stage, and get the limit of the numerator as -2 and the limit of the denominator as 0, they do another derivative. This is only valid if the numerator and denominator are both 0 (or both infinity). Once we've done the first derivatives, we're done.

Prehaps more interesting is NPCurmudgeon's solution where he rewrites the function using series expansions and arrives at the solution quickly and elegantly.

On a vaguely related note, I found myself contemplating some function that was described by my Calc teacher in high school as being unintegrable (in that there wasn't any simply defined function for which g'(x)=f(x)). I had one of those moments of inspiration where I realized that this could probably be dealt with through taylor expansions. You'd end up with a nasty looking infinite series, but it would at least allow for easier estimations of the definite integral than using the trapezoid method or one of its close relatives. I probably learned this in one of the many calc classes that I took all those years ago, but it was a nice revelation as I was thinking about it. Now all I need is one of those unintegrable functions so I can tackle the matter.

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