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authorPaul Duncan <pabs@pablotron.org>2017-11-07 23:45:13 -0500
committerPaul Duncan <pabs@pablotron.org>2017-11-07 23:45:13 -0500
commit814e716cf003500ada840fcf7cc2c6cada41e1cb (patch)
tree9c5f3ea3d3bfdafe7272b8c805fe493c7b86a671 /htdocs
parent9a98e13af98db2801430c5c4062a822b66ad74a2 (diff)
downloadmathy-814e716cf003500ada840fcf7cc2c6cada41e1cb.tar.bz2
mathy-814e716cf003500ada840fcf7cc2c6cada41e1cb.zip
remove old help
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</a><!-- btn -->
<ul id='help' class='dropdown-menu'>
- <li class='dropdown-header'>
- Examples
- </li>
-
- <li>
- <a
- href='#'
- class='example'
- data-text='
- \lim_{x \to \infty}{\frac{1}{x^2}}
- '
- >1. Some Limit</a>
- </li>
-
- <!-- li>
- <a
- href='#'
- class='example'
- data-text='
- \begin{align*}
- &= \int_0^2{x^2 + 5x + 2}\,\text{d}x \\
- &= \int{x^2 + 5x + 2}\,\text{d}x \\
- &= \frac{1}{3}x^3 + \frac{5}{2}x^2 + 2x + c \\
- &= \frac{1}{3}2^3 + \frac{5}{2}2^2 + 2\times2 -
- (\frac{1}{3}0^3 + \frac{5}{2}0^2 + 2\times0) \\
- &= \frac{8}{3} + \frac{20}{2} + 4 \\
- &= 14 + \frac{8}{3} \\
- &= \frac{50}{3}
- \end{align*}
- '
- >Test 2</a>
- </li -->
-
- <li>
- <a
- href='#'
- class='example'
- data-text='
-\text{Quadratic Formula} \\
-x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
- '
- >2. Quadratic Formula</a>
- </li>
-
- <li>
- <a
- href='#'
- class='example'
- data-text='
-\text{Cross Product via Matrix Determinant} \\
-
-\begin{align*}
- \vec{a} \times \vec{b} & = \begin{vmatrix}
- \hat{i} & \hat{j} & \hat{k} \\
- \vec{a}_x & \vec{a}_y & \vec{a}_z \\
- \vec{b}_x & \vec{b}_y & \vec{b}_z
- \end{vmatrix} \\
-
- & =
- \begin{vmatrix}
- \vec{a}_y & \vec{a}_z \\
- \vec{b}_y & \vec{b}_z
- \end{vmatrix} \hat{i} -
-
- \begin{vmatrix}
- \vec{a}_x & \vec{a}_z \\
- \vec{b}_x & \vec{b}_z
- \end{vmatrix} \hat{j} +
-
- \begin{vmatrix}
- \vec{a}_x & \vec{a}_y \\
- \vec{b}_x & \vec{b}_y
- \end{vmatrix} \hat{k} \\
-
- & =
- (\vec{a}_y\vec{b}_z - \vec{a}_z\vec{b}_y)\hat{i} -
- (\vec{a}_x\vec{b}_z - \vec{a}_z\vec{b}_x)\hat{j} +
- (\vec{a}_x\vec{b}_y - \vec{a}_x\vec{b}_y)\hat{k} \\
-
- & =
- \langle
- \vec{a}_y\vec{b}_z - \vec{a}_z\vec{b}_y\text{, }
- \vec{a}_x\vec{b}_z - \vec{a}_z\vec{b}_x\text{, }
- \vec{a}_x\vec{b}_y - \vec{a}_y\vec{b}_z
- \rangle \\
-
- \vec{a} & = \langle2, 1, -1\rangle \\
- \vec{b} & = \langle-3, 4, 1\rangle \\
- \vec{a} \times \vec{b} & = \langle
- (1)(1) - (-1)(4),
- (2)(1) - (-1)(-3),
- (2)(4) - (1)(-3)
- \rangle \\
-
- & = \langle
- 5, 5, 11
- \rangle \\
- \vec{b} \times \vec{a} & = \langle
- (4)(-1) - (1)(1),
- (-3)(-1) - (1)(2),
- (-3)(1) - (4)(2)
- \rangle \\
- & = \langle
- -5, -5, -11
- \rangle
-\end{align*}
- '
- >3. Cross Product</a>
- </li>
-
- <li>
- <a
- href='#'
- class='example'
- data-text="
-\text{Derivative Rules} \\
-
-\begin{align*}
-% sum/difference rule
-\frac{\text{d}}{\text{d}x} \,
-f(x) \pm g(x) &=
-\frac{\text{d}}{\text{d}x} \, f(x) \pm
-\frac{\text{d}}{\text{d}x} \, g(x) &
-\text{Sum/Difference Rule} \\
-
-% constant factor rule
-\frac{\text{d}}{\text{d}x} \,
-k f(x) &=
-k \frac{\text{d}}{\text{d}x} \, f(x) &
-\text{Constant Factor Rule} \\
-
-% constant rule
-\frac{\text{d}}{\text{d}x} \,
-k &=
-0 &
-\text{Constant Rule} \\
-
-% power rule
-\frac{\text{d}}{\text{d}x} \,
-x^n &=
-nx^{n-1} &
-\text{Power Rule} \\
-
-% exponent rule
-\frac{\text{d}}{\text{d}x} \,
-b^x &=
-b^xln(b) &
-\text{Exponent Rule} \\
-
-% chain rule
-\frac{\text{d}}{\text{d}x} \,
-f(g(x)) &=
-% (f \cdot g)(x) &=
-f'(g(x))g'(x) &
-\text{Chain Rule} \\
-
-% product rule
-\frac{\text{d}}{\text{d}x} \,
-f(x)g(x) &=
-f'(x)g(x) + f(x)g'(x) &
-\text{Product Rule} \\
-
-% quotient rule
-\frac{\text{d}}{\text{d}x} \,
-\frac{f(x)}{g(x)} &=
-\frac{f'(x)g(x) - f(x)g'(x)}{g(x)^2} &
-\text{Quotient Rule} \\
-
-% logarithm rule
-\frac{\text{d}}{\text{d}x} \,
-log_b{x} &=
-\frac{1}{x ln(b)} &
-\text{Logarithm Rule} \\
-
-\end{align*}
-"
- >4. Derivative Rules</a>
- </li>
-
- <li>
- <a
- href='#'
- class='example'
- data-text="
-% https://math.vanderbilt.edu/schectex/courses/cubic/
-\text{The Cubic Formula} \\
-\begin{align*}
-% first term
-x &= \sqrt[3]{
- % first term, first subterm
- \left (
- \frac{-b^3}{27a^3} +
- \frac{bc}{6a^2} -
- \frac{d}{2a}
- \right )
-
- +
-
- \sqrt{
- % first term, second subterm
- \left (
- \frac{-b^3}{27a^3} +
- \frac{bc}{6a^2} -
- \frac{d}{2a}
- \right )^2
-
- +
-
- % first term, third subterm
- \left (
- \frac{c}{3a} -
- \frac{b^2}{9a^2}
- \right )^3
- }
-} \\
-
-&+
-
-% second term
-\sqrt[3]{
- % first term, second subterm
- \left (
- \frac{-b^3}{27a^3} +
- \frac{bc}{6a^2} -
- \frac{d}{2a}
- \right )
-
- -
-
- \sqrt{
- % second term, second subterm
- \left (
- \frac{-b^3}{27a^3} +
- \frac{bc}{6a^2} -
- \frac{d}{2a}
- \right )^2
-
- +
-
- % second term, third subterm
- \left (
- \frac{c}{3a} -
- \frac{b^2}{9a^2}
- \right )^3
- }
-} \\
-
-&-
-
-% third part
-\frac{b}{3a}
-\end{align*}
- "
- >5. Cubic Formula</a>
- </li>
- <li>
- <a
- href='#'
- class='example'
- data-text="
-\text{Linear Regression} \\
-
-\begin{align*}
- m &= \frac{
- \sum(x_i - \bar{x})(y_i - \bar{y} )
- }{
- \sum(x_i - \bar{x})^2
- } \\
-
- b &= \bar{y} - m\bar{x} \\
-
- y &= mx + b
-\end{align*}
- "
- >6. Linear Regression</a>
- </li>
- <li class='divider'></li>
</ul><!-- dropdown-menu -->
</div><!-- btn-group -->