| Line 20: | Line 20: | ||
<math>\int\frac{du}{\sqrt{a^2-u^2}}=\sin^{-1}\frac{u}{a} + C</math> | <math>\int\frac{du}{\sqrt{a^2-u^2}}=\sin^{-1}\frac{u}{a} + C</math> | ||
| + | |||
| + | <math>\frac{\pi}{4}= 1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\cdots</math> | ||
| + | |||
| + | <math> = \sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n-1}</math> | ||
Revision as of 10:41, 13 October 2008
Just in case so you don't have to look them up in your book or whatever. And so I can learn how to use Latex!
Hyperbolic Functions
- $ \sinh(x) = \frac{e^x - e^{-x}}{2} $
- $ \cosh(x) = \frac{e^x + e^{-x}}{2} $
- $ \tanh(x) = \frac{\sinh(x)}{\cosh(x)} = \frac{e^x - e^{-x}}{e^x + e^{-x}} $
- $ \coth(x) = \frac{\cosh(x)}{\sinh(x)} = \frac{{e^x + e^{-x}}}{{e^x - e^{-x}}} $
- $ \text{sech}(x) = \frac{1}{\cosh(x)} = \frac{2}{{e^x + e^{-x}}} $
- $ \text{csch}(x) = \frac{1}{\sinh(x)} = \frac{2}{e^x - e^{-x}} $
Idryg 20:10, 11 October 2008 (UTC)
Basic Integration Formulas
$ \int\frac{du}{\sqrt{a^2-u^2}}=\sin^{-1}\frac{u}{a} + C $
$ \frac{\pi}{4}= 1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\cdots $
$ = \sum_{n=1}^\infty \frac{(-1)^{n+1}}{2n-1} $
