User:WraithM/math

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[edit] Test

\int {d \over dx} f(x) \, dx = f(x)


[edit] Proof of Volume and Surface Area of a Sphere

sin \, \theta = {x \over r}
x = r sin \, \theta
2 \int_0^{\pi \over 2} {2 \pi r \, sin \theta \, r} d\theta
4 \pi r^2 \int_0^{\pi \over 2} {sin \theta} \, d\theta = 4 \pi r^2
\int {4 \pi r^2} \, dr = 4 \pi \int {r^2} \, dr = {4 \over 3} \pi r^3

[edit] Partial Derivatives Test

f(x,y) = x2 + y2
\frac{\partial}{\partial x} f(x,y) = 2x


Goofing around with second partial derivatives and double integrals.
f(x,y) = x2y + y2x
\frac{\partial}{\partial x} f(x,y) = 2xy + y^2
\frac{\partial^2}{\partial x \partial y} f(x,y) = 2x + 2y
\iint {2x + 2y} \, dxdy = x^2y + y^2x = f(x,y)
\iint {\frac{\partial^2}{\partial x \partial y} f(x,y)} \, dxdy = f(x,y)

[edit] Chemistry

Percent error Percent Error = \frac{(.507-.512)}{.512} \times 100% = -97%

[edit] Lindsay

The\,Amount\,of\,Love\,Matthew\,Wraith\,Has\,for\,Lindsay\,Preseau = (\displaystyle\lim_{x\to\infty}{\displaystyle\prod_{n=1}^\infty{\displaystyle\sum_{j=1}^{\infty}{x^{n\infty}+\mathbb{R}^{\mathbb{C}+\infty j x n})!}}}

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