Question

\(\LaTeX\) workspace.

Answer 1

\[f'(x) = \lim_{h\to 0}\frac{f(x+h)-f(x)}{h}\]
\[f(x)=x^3\]
\[h~means~\Delta x = x_2-x_1 \Rightarrow x_2 = x_1 + \Delta x\]
Odd the \implies command doesn't work here :-(.

Answer 2

Does \(\LaTeX\) handle Japanese fonts?
\[貴社ますますご盛栄のこととお慶び申し上げます。平素は格別のご高配を賜り、厚く御礼申し上げます。\]

Answer 3

```
貴社ますますご盛栄のこととお慶び申し上げます。平素は格別のご高配を賜り、厚く御礼申し上げます。
```

Answer 4

Yup, plain text is much cleaner.

Answer 5

Taylor's expansion:
\[\Large e^x=1+\dfrac{x}{1!}+\dfrac{x^2}{2!}+\dfrac{x^3}{3!}+⋯,-∞<x<∞\]

Answer 6

How to write radicals?
\[\Large \sqrt[n]{x}\]
\[\large 2~\sqrt[3]{x+2}+4\]

Answer 7

\[
\Phi(\mathbf{x}_1,\mathbf{x}_2,\dots\mathbf{x}_N) = \frac{1}{\sqrt{N!}}\left|
\begin{matrix} \chi_1(\mathbf{x}_1) & \chi_2(\mathbf{x}_1) & \cdots & \chi_N(\mathbf{x}_1) \\
\chi_1(\mathbf{x}_2) & \chi_2(\mathbf{x}_2) & \cdots & \chi_N(\mathbf{x}_2) \\
\vdots & \vdots & \ddots & \vdots \\
\chi_1(\mathbf{x}_N) & \chi_2(\mathbf{x}_N) & \cdots & \chi_N(\mathbf{x}_N)
\end{matrix} \right|
\]

Answer 8

\(\text{Math Settings > Math Render(er) > SVG}\)
SVG looks cleaner for me, anyone else?

Answer 9

\[\newcommand{\distanceformula}{d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}\]
\[\distanceformula\]
```
\[\newcommand{\distanceformula}{d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}\]
\[\distanceformula\]
```
\[
\newcommand{\binomialtheorem}{(x+a)^n~=~\sum_{k=0}^n~\binom{n}{k}~x^k~a^{n-k}}
\]
\[\binomialtheorem\]
```
\[\newcommand{\binomialtheorem}{(x+a)^n~=~\sum_{k=0}^n~\binom{n}{k}~x^k~a^{n-k}}\]
\[\binomialtheorem\]
```

Answer 10

\[\def \bangle{ \atopwithdelims \langle \rangle}\]

Answer 11

Blank post :-).

Answer 12

\[\color{red}{\ll\ll\ll\ll\ll\ll\ll\ll\ll\ll\ll\ll\ll\ll\ll\ll~\gg\gg\gg\gg\gg\gg\gg\gg\gg\gg\gg\gg\gg\gg\gg\gg}\]
\[\mathcal{\text{From love comes hatred and all the better things of life. -Lanuage Enthusiast}}\]
\[\mathcal{\qquad\qquad\qquad\text{I want to learn all about mathematics and science.}}\]
\[\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\color{red}{\tilde{*}}\color{green}{\tilde{*}}\]
\[\Huge \mathcal{\color{green}{\text{I wish you a merry Christmas.}}}\]
\[\color{red}{\quad \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow \nearrow\nwarrow }\]
\[\it{\text{Wishlist:}}\]
\[\it{\text{ I wish for someone to teach me all about mathematics in one day :3}}\]
\[\it{\text{ I wish for someone to teach me all about science in one day :3}}\]
\[\qquad \qquad \qquad \qquad \qquad \qquad \it{\text{ I wish to be smarter :3}}\]
\[\bf{\text{Please Santa will you grant my wish? I have been a good child...}}\]

Answer 13

I have way to much time on my hands...

Answer 14

Odd, there is no word wrap for \(\LaTeX\).

Answer 15

I am not a good child, I used \bf when I should of used \bfseries.
Though in my defense, MathJax does not support that command.
Bolded text: \[\textbf{This is bolded text.}\]
Using:
```
\textbf
```
Instead of:
```
\bf
```

Answer 16

Trigonometry notes:
\[\textbf{SOH CAH TOA:}\]
\[SOH = \sin \theta = \dfrac{Opposite}{Hypotenuse}\]
\[CAH = \cos \theta = \dfrac{Adjacent}{Hypotenuse}\]
\[TOA = \tan \theta = \dfrac{Opposite}{Adjacent}\]
\[\textbf{Pythagorean Identities:}\]
\[\sin^2 \theta + cos^2 \theta = 1\]
\[tan^2 \theta + 1 = sec^2 \theta\]
\[cot^2 \theta + 1 = csc^2 \theta\]
\[\textbf{Ratio Identities:}\]
\[\tan x=\dfrac{sin~x}{cos~x}\]
\[ \cot x =\dfrac{cos~x}{sin~x}\]
\[\textbf{Odd/Even Identities:}\]
\[\sin(–x) =~–\sin x\]
\[\cos(–x) = \cos x\]
\[\tan(–x) =~–\tan x\]
\[\csc(–x) =~–\csc x\]
\[\sec(–x) = \sec x\]
\[\cot(–x) =~–\cot x\]

Answer 17

Algorithm in which the given term \(m\) generates a triple: \[II(M) = (Ψ, U, Η)\]
\[\lambda -Calculus\]

Answer 18

It was shown that for the Z-module of these polynomials, the sequence of powers \(x^n\) is not a basis, whether the Newton Expansion Theorem shows that a natural basis
is the so-called “binomial basis”, that is, the sequence of the polynomials:
\[\beta_n(x)=\binom{x}{n}\]
Link for the notes: https://en.wikipedia.org/wiki/Umbral_calculus

Answer 19

Japanese support depends on the text editor.
http://www.latex-community.org/forum/viewtopic.php?f=48&t=4887

Answer 20

We are going from Manayunk to Wilmington and from Wilmington to Manayunk.
d (distance) must be constant during the whole trip.
r (rate) we know is \(\dfrac{2}{3}\).

Supposedly according to: https://en.wikipedia.org/wiki/Proportionality_(mathematics)

We be take the inverse of that?
\[\dfrac{2}{3} \implies \dfrac{3}{2} \implies 1.5\]

Manayunk to Wilmington:
\[100\times1.5 \div (1.5 + 1.5) = 60%\]

\[100 \times 1.5\] So we can have a percentage.
\[1.5 + 1.5\] Time driven there. (Manayunk to Wilmington and from Wilmington to Manayunk).

Answer 21

That answer is for this question for future references: http://openstudy.com/study#/updates/52d1dff5e4b01e5fc1df427a