User:Tetraglot/Sandbox

$$ \begin{align} {\operatorname{d}\over\operatorname{d}x} \int_{0}^{x} g(x) f(t) dt \\ = \left[ g(x) f(t) {\operatorname{d}t\over\operatorname{d}x} \right]_0^x \\ = g(x) f(x) t\prime(x) - g(x) f(0) t\prime(0) \end{align}

$$

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🇲🇨🇮🇩 🇪🇸🇫🇷🇯🇵🇵🇪🇹🇿🇩🇪🇸🇪 My sandbox! Yay! Please do not edit this. /3V2{,wk%-X! http://requests.wikia.com/index.php?title=Engrish&action=purge

$$ E = Cp \cdot m \cdot \Delta T = 0.0564 \frac{Cal}{g ^\circ C} \cdot 50.0g \cdot (50.0-20.0)^\circ C = 84.6 cal $$

$$

-10^\circ F = \left [ \frac{(-10-32) \cdot 5}{9} \right ]^\circ C = \left ( \frac{-42 \cdot 5}{9} \right ) ^\circ C = -23.\overline{3}^\circ C = -20 ^\circ C $$

$$ -10^\circ C = \left ( \frac{-10 \cdot 9}{5} + 32 \right )^\circ F = (-18 + 32) ^\circ F = 14^\circ F

$$

$$ 165 Cal = 165 Cal \cdot \frac{1000 cal}{1 cal} \cdot \frac{4.184 j}{1 cal} = 690,360 j = 690. \times 10^5 j $$

$$f(x) = \begin{cases} -x, & -5\le x\le 1 \\ \frac{3}{10}x-\frac{3}{5}, & -1\le x\le 9 \end{cases}$$

$$ f(x) = \begin{cases} f(x)_1, & \mbox{domain }_1 \\ f(x)_2, & \mbox{domain }_2 \end{cases} $$

$$ f(x) = \begin{cases} ax, & x\ge h \\ -ax, & x<h \end{cases} $$