## Mathochism: Getting fundamental

**One woman’s attempt to revisit the math that plagued her in school. But can determination make up for 25 years of math neglect?
**

Back when I took geometry (and got As, sniff), Uchitel told us there were only really two problems in calculus.

One involved the fundamental theorem of calculus. Because of Uchitel’s ebullient way of explaining it, I’ve been really looking forward to studying it in this class.

We started on it Thursday, and really went into it today.

And… I feel a bit like the creatures who waited millions of years to be told the meaning of life, the universe and everything, only to get “42″ as an answer.

Not that the fundamental theorem of calculus isn’t just charming and fabulous, or anything. It’s just that I expected something more — fancy. Something longer. Something truly mind-boggling.

That is not to say it isn’t mind-boggling. It must be, right? Just because I don’t find it particularly befuddling right now means nothing. If calculus has taught me anything, it’s that the bulk of the knowledge is under the surface, iceberg-style. I’m getting better at sticking my head under the waterline, and I can stay under longer, but not long enough to keep up without freezing on exams.

And speaking of getting stuck, I recently discovered we are not covering L’Hopital’s rule this semester.

Disappointed!

I mean, even if I hadn’t screwed the polynomial this semester, I still wasn’t planning to take Calc II. This is truly the end of the line. And yes, I know I can study on my own, though I am not an autodidact when it comes to math.

Does Calc I ever cover that? Or is it just my college? I think maybe, since I have been perusing other sources this semester. In some books, L’Hopital appears after derivatives. And goodness knows I could have used the ‘ol Marquis’ help when I was evaluating trig limits.

Oh well. Time to put on the wetsuit and hold my breath — the icescapes are waiting.

*All text copyrighted by A.K. Whitney, and cannot be used without permission.
*

We cover L’Hopital’s Rule in both Calculus I and II, since it’s useful for some limits encountered in Calc I, but it’s also something that a lot of students who took their first calculus class at another school may not have been taught before.

Unfortunately, you won’t fully realize the magic of the Fundamental Theorem of Calculus unless you study Calc II. But really, the idea that slope (or rate) given by a derivative is related to the area under a curve given by an integral is not at all intuitive, but it is amazingly useful! FTC is the only reason we can even bother with integrals, that great mainstay of modern mathematics.

You cover it? I’m jealous! It seems like such a cool technique.

It really is. It’s so useful that at the beginning of Calc I (before we cover L’Hospital’s Rule), I can never remember off the top of my head how to do most limits without it. Every other way of proving lim(x->0)sinx/x=1 is just silly.

Sigh. So much suffering could have been prevented…

The Wikipedia page on L’Hôpital’s rule has a pretty good discussion, with several examples: http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule

Even if you don’t cover it in class, I think you should be able to get it from there.