Bogleheads:Sandbox

A radical formula: $$ \sqrt[3]{x^3+y^3 \over 2}$$

Partial: $${\partial^2\over\partial x_1\partial x_2}y$$



\operatorname{E}[X] = x_1p_1 + x_2p_2 + \ldots + x_kp_k \;. $$

Changed to E[Y]:

\operatorname{E}[Y] = x_1p_1 + x_2p_2 + \ldots + x_kp_k \;. $$

$$ \begin{align} {marginal\ tax\ rate\ at\ income\ of\ $20,000} & = \frac{tax(20,000 + 100) - tax(20,000)}{(20,000 + 100) - (20,000)} \\ \\ {marginal\ tax\ rate(I)}&= \frac{tax(I + \Delta) - tax(I)}{\Delta}\\ \\ \frac{df(x)}{dx}&=\lim_{\delta\rightarrow \infty} \frac{(f(x+\delta)-f(x))}{\delta} \end{align} $$

Changed to 0:

$$ \begin{align} {marginal\ tax\ rate\ at\ income\ of\ $20,000} & = \frac{tax(20,000 + 100) - tax(20,000)}{(20,000 + 100) - (20,000)} \\ \\ {marginal\ tax\ rate(I)}&= \frac{tax(I + \Delta) - tax(I)}{\Delta}\\ \\ \frac{df(x)}{dx}&=\lim_{\delta\rightarrow 0} \frac{(f(x+\delta)-f(x))}{\delta} \end{align} $$