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− | {{AoPSWiki:Sandbox/header}} <!-- Please do not delete this line -->
| + | =A= |
− | In the computer world, a '''sandbox''' is a place to test and experiment -- essentially, it's a place to play.
| + | ==B== |
− | | + | ===C=== |
− | This is the AoPSWiki Sandbox. Feel free to experiment here.
| + | ====E==== |
− | | + | Apple |
− | Warning: anything you place here is subject to deletion without notice.
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− | | |
− | === Sandbox Area === | |
− | <asy>
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− | draw((0,0)--(3,9),black);
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− | label("$71^\circ$",(0,0),NE);
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− | draw((3,9)--(6,0),black);
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− | label("$71^\circ$",(6,0),NW);
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− | draw((0,0)--(6,0),black);
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− | label("$38^\circ$",(3,8),S);
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− | dot((0,0));
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− | dot((3,9));
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− | dot((6,0));
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− | draw((-1,7)--(2.3,5.9),black);
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− | draw((-1,6)--(2,6),red);
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− | label("$19^\circ$",(1,6),NW);
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− | </asy>
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− | | |
− | <math>\lim_{x\to0}\frac{a}{x}</math>
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− | | |
− | The characteristic polynomial <math>f(\lambda)</math> of the
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− | <math>3 \times 3</math> matrix
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− | <math>
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− | \left(
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− | \begin{array}{ccc}
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− | a & b & c \\
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− | d & e & f \\
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− | g & h & i \end{array}
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− | \right)</math>
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− | is given by the equation
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− | <math> f(\lambda)
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− | = \left| | |
− | \begin{array}{ccc}
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− | \lambda - a & -b & -c \\
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− | -d & \lambda - e & -f \\
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− | -g & -h & \lambda - i \end{array}
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− | \right|.</math>
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− | <math>e^{\pi \cdot i}=-1</math>
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− | For <math>x=3_i</math>, <math>x^2=-9</math>.
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