User:Akuyume/Sandbox

Akuyume's Sandbox!!

Welcome to Akuyume's sandbox/playground! Feel free to look but Akuyume might not want you to touch his toys (he's greedy, ok?), so if you want to experiment see the public sandbox.

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• See WP:MATH for a glossary of the syntax.

Limits and fractions woohoo!

$\lim _{x\to -\infty }{\dfrac {2x}{\sqrt {x^{2}+1}}}*{\dfrac {\tfrac {1}{x}}{\tfrac {1}{x}}}=\lim _{x\to -\infty }{\dfrac {2}{1+{\sqrt {\tfrac {1}{x}}}}}={\dfrac {2}{1+0}}=2$

Derivatives

${\begin{aligned}g(x)=(x+3)^{\tfrac {1}{3}}\\c=-3\\g'(-3)=\lim _{x\to -3}{\dfrac {g(x)-g(c)}{x-c}}\\g'(-3)=\lim _{x\to -3}{\dfrac {(x+3)^{\tfrac {1}{3}}-0}{x+3}}\\g'(-3)=\lim _{x\to -3}{\dfrac {1}{x+3^{\tfrac {2}{3}}}}\\\therefore g'(-3)\uparrow \end{aligned}}$

Signature

It was recently brought to my attention that my signature renders differently in Internet Explorer than Firefox and Opera, so I've set out to see if I can manage to forge a new version which will render mostly identically in all modern web browsers.

Old

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. akuyume^T_C Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

New

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. akuyume^T_C Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.