User:Maxdamantus/tex

$$e = \sum^\infty_{i=0} \frac{1}{i!}$$ $$1 + \sum_{i=0}^5 16^i$$ $$ \left( \begin{array}{c} \left( \begin{array}{c} \mbox{Welcome} \\ \mbox{Time: 13:37pm} \end{array} \right) \\ \left( \begin{array}{ccc} (1) & (2) & (3) \\   (4) & (5) & (6) \\    (7) & (8) & (9) \\        &     & (0)  \end{array} \right) \end{array} \right)$$ $$\frac{45}2+t_P$$ I believe you mean $$22.5 + t_P$$, Max. $$(a+b)^n = \sum_{i=0}^{\infty} { n \choose i } \cdot a^{n-i} \cdot b^n $$ -- $$f_{n+1}\left( x \right)\; =\; f_{n}\left( x \right)+\left( x+1 \right)\left( -x \right)^{n+1}\; \; \; \; \; \; g_{n+1}\left( x \right)\; =\; 1+x^{n+2}$$ $$f_{n+1}\left( x \right)=f_{n}\left( x \right)+\left( x+1 \right)\left( -x \right)^{n+1}$$

$$ ax^2 + bx + c = a\left(x + \frac{b}{2a}x\right)^2 - \left(\frac{b}{2a}x\right)^2 + c $$ $$\lim_{x \to 1}\frac{\lfloor{x^2}\rfloor-\lfloor{x}\rfloor}{x - 1}$$

$$ {\delta_{1 \over f} \over {1 \over f}} = {\delta_1 \over 1} + {\delta_f \over f} = {\delta_{1 \over d_i} \over d_i} + {\delta_{1 \over d_o} \over d_o} $$

$$\int_i^fdW = \int_i^f{\vec{F} \cdot d\vec{s}}$$

$$\int_0^1{xe^{-x^2}}dx = -{1 \over 2e^2}$$

$$\delta f(x_1, x_2, ..., x_n) = \sqrt{\sum_{i = 1}^n \left({\partial f \over \partial x_i} \delta x_i\right)^2}$$

$$\sum_{i = 1}^n \prod_{j = 1}^n D_{ij}(f)$$ where $$D_{ij}(f) = f', i = j, \text{ or } f, i \neq j$$

$$ \dot{\vec{r}} = \vec{r_0} + \int_{t_1}^{t_2} \frac{G m_2 (\vec{r_2} - \vec{r_1})}{||\vec{r_2} - \vec{r_1}||^3} + \int_{t_1}^{t_2} \frac{G m_3 (\vec{r_3} - \vec{r_1})}{||\vec{r_3} - \vec{r_1}||^3} + \ldots + \int_{t_1}^{t_2} \frac{G m_n (\vec{r_n} - \vec{r_1})}{||\vec{r_n} - \vec{r_1}||^3}

$$ $$ \ddot{\vec{r_1}} = \frac{G m_2 ( \vec{r_2} - \vec{r_1} )}{||\vec{r_2} - \vec{r_1}||^3} + \frac{G m_2 ( \vec{r_3} - \vec{r_1} )}{||\vec{r_3} - \vec{r_1}||^3} + \ldots + \frac{G m_n ( \vec{r_n} - \vec{r_1} )}{||\vec{r_n} - \vec{r_1}||^3} $$