Warning: math geek alert. Read at your own discretion.
I swear, everyday in Math 101 there's something new and interesting. Last class we were doing something I was looking forward to for a while - arc lengths. Ever since calc 12 I was wondering how the heck you'd do something like that and even recently I got a bit farther (figured out that dL = sqrt(dx^2 + dy^2)), but didn't know how to finish the calculation. Well, we just learned it last Wednesday and I'm amazed at how it works, because you need both a derivative and an integral in order to figure it out.
Well, today we did inverse trig functions. We did them last year, but never got into how exactly d(arctan x)/dx = (1+x^2)^-1, etc. It's just so cool how it works, using the fact that f(g(x)), where g is the inverse of f, is equal to x. I can't wait for taylor expansions and integration by parts.
Anyway, I'm done being a complete math nerd now.
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