Wednesday, March 31, 2010

(yes, another batman reference.)

somehow i'm prone to making references to the dark knιght in my classes.

today i described the proof of one of l'hôpital's rules as similar to the first scene, where they have the bank robbery:

you can't rob a bank by yourself, so you need a gang -- say, another gunman who watches the crowd, as well as a getaway driver -- but say that you want to keep all the money to yourself ..

here, we are $x$; the getaway driver is $a$, and the other gunman is $c$, where we use a mean-value theοrem of the form

$$\frac{f(x)-f(a)}{g(x)-g(a)} \;=\; \frac{f'(c)}{g'(c)}.$$

let's just say that, to prove the theorem, we want to get rid of $a$ and $c$ .. (-:

the students seemed amused by it, even by the end of the proof.