LaTex Coding

Thank you Alan,

This is where I want it.  As more bits and peices get added it would be good if it gets cleaned up into a neater thread but for now this is great.

-----------------------------

More limits

$$\small{\text{$\lim \limits_{x \rightarrow \infty } 9\cdot \dfrac{(x+4)(x-2)}{(x-4)(x-6)} =\lim \limits_{x \rightarrow \infty } 9\cdot \dfrac{x^2+2x-8}{x^2-10x+24}=\lim \limits_{x \rightarrow \infty } 9\cdot \dfrac{ \dfrac{x^2}{x^2}+\dfrac{2x}{x^2}-\dfrac{8}{x^2}}{ \dfrac{x^2}{x^2}-\dfrac{10x}{x^2}+\dfrac{24}{x^2}}=\lim \limits_{x \rightarrow \infty } 9\cdot \dfrac{ 1 + \dfrac{2}{x}-\dfrac{8}{x^2}}{ 1 - \dfrac{10}{x}+\dfrac{24}{x^2}}= 9\cdot \dfrac{ 1 }{ 1 }=9 $}}\\\\$$

\small{\text{$\lim \limits_{x \rightarrow \infty } 9\cdot \dfrac{(x+4)(x-2)}{(x-4)(x-6)}

=\lim \limits_{x \rightarrow \infty } 9\cdot \dfrac{x^2+2x-8}{x^2-10x+24}

=\lim \limits_{x \rightarrow \infty } 9\cdot \dfrac{ \dfrac{x^2}{x^2}+\dfrac{2x}{x^2}-\dfrac{8}{x^2}}{ \dfrac{x^2}{x^2}-\dfrac{10x}{x^2}+\dfrac{24}{x^2}}

=\lim \limits_{x \rightarrow \infty } 9\cdot \dfrac{ 1 + \dfrac{2}{x}-\dfrac{8}{x^2}}{ 1 - \dfrac{10}{x}+\dfrac{24}{x^2}}= 9\cdot \dfrac{ 1 }{ 1 }=9 $}}\\\\

I've discovered how to put labels on a summation sign correctly.  For example:

\begin{document}

Starting with:
$$\frac{3x+h}{x+h}$$

Limit as h tends to zero:
$$\lim_{h\rightarrow0}\frac{3x+h}{x+h}$$

\end{document}

produces

$$Starting with:
$$\frac{3x+h}{x+h}$$

Limit as h tends to zero:
$$\lim_{h\rightarrow0}\frac{3x+h}{x+h}$$$$

However, if you leave out the begin{} and end{} and the $$ signs you get (after ignoring the text and first expression):

$$\lim_{h\rightarrow0}\frac{3x+h}{x+h}$$

I don't know if you want this in this thread Melody.  If not I'll delete it and create a separate thread.

Here are some arrow comands that may be useful

http://access2science.com/latex/Arrows.html

 Useful symbols

http://www.math.sinica.edu.tw/tex/aassymbols.pdf

http://omega.albany.edu:8008/Symbols.html

Ninja found this one - it seems quite comprehensive (1/8/14)

http://latex.wikia.com/wiki/List_of_LaTeX_symbols

I just made this up in Texmaker.

It won't work in here at the moment because some of the packages are missing.

Another thing to talk to Andre about - this is often a problems.

More limits by Heureka here

http://web2.0calc.com/questions/if-x-0-what-is-the-qotient-of-40-x#r106714

 I tried the code below but it didn't work  

HEUREKA HAS SHOWN ME HOW TO DO IT    (14/10/14)

\sum \limits_{n=1}^{\infty} :            $$\sum \limits_{n=1}^{\infty}$$

---------------------------------------------------------------------------------------------------- 

\displaystyle \lim_{x\rightarrow -1}\;\;\dfrac{|x+1|}{x^2+1}

$$\displaystyle \lim_{x\rightarrow -1}\;\;\dfrac{|x+1|}{x^2+1}$$

-----------------------------------------------------------------------------------------------------

More ideas from LancelotLink

\ V(x)=\dfrac{W}{m}\ = \dfrac{1}{m}\int \limits_{\infty}^{x}\ F\ dx =\dfrac{1}{m}\int \limits_{\infty}^{x}\dfrac{GmM}{x^2}dx=-\dfrac{GM}{x}

$$\ V(x)=\dfrac{W}{m}\ = \dfrac{1}{m}\int \limits_{\infty}^{x}\ F\ dx =\dfrac{1}{m}\int \limits_{\infty}^{x}\dfrac{GmM}{x^2}dx=-\dfrac{GM}{x}$$

I posted a page of latex before and now it is all gone!

I must of forgotten to hit "Publish" I am a drongo!  I'll have to do it again - Later.

(Drongo is Australian slang meaning 'a fool', but when used like this it is light hearted.  

It is also the name of an Australian bird.)

I am just going to add examples here.

-------------------------------------------------------------------------

(2x+7)(4x-1)\leq 0 \Rightarrow \left[-\dfrac 7 2 \leq x \leq \dfrac 1 4 \right]

$$(2x+7)(4x-1)\leq 0 \Rightarrow \left[-\dfrac 7 2 \leq x \leq \dfrac 1 4 \right]$$        By Rom

-------------------------------------------------------------------------

\left[-\dfrac 7 2 \leq x \leq \dfrac 1 4 \right] \bigcup \left\{\dfrac 1 2 \right\}

$$\left[-\dfrac 7 2 \leq x \leq \dfrac 1 4 \right] \bigcup \left\{\dfrac 1 2 \right\}$$    By Rom

Heureko's LaTex

http://web2.0calc.com/questions/what-is-mod  

latex code:

\\\boxed{(a\bmod b)=a-b\lfloor\frac{a}{b}\rfloor}\\
\\
Example: \quad 299\bmod 12=299-12*\lfloor\frac{299}{12}\rfloor\\ 
= 299-12*24=299-288=11

$$\lfloor \dots \rfloor = floor function$$

latex code:

\lfloor \dots \rfloor = floor function

output:

$$\\\boxed{(a\bmod b)=a-b\lfloor\frac{a}{b}\rfloor}\\
\\
Example: \quad 299\bmod 12=299-12*\lfloor\frac{299}{12}\rfloor\\
= 299-12*24=299-288=11

\lfloor \dots \rfloor = floor function

latex code:

\lfloor \dots \rfloor = floor function$$

This is posted on the Latex thread in the sticky notes.

$$\begin{array}{rlllr}
( x^3&+4x^2&+x& -6)&:(x-1)=\textcolor[rgb]{1,0,0}{x^2}\textcolor[rgb]{0,0,1}{+5x}\textcolor[rgb]{0,1,0}{+6}\\
\textcolor[rgb]{1,0,0}{{\underline{-(x^3}}&\textcolor[rgb]{1,0,0}{\underline{-x^2)}}}&&&\\
0&+5x^2&+x\\
&\textcolor[rgb]{0,0,1}{\underline{-(5x^2}}&\textcolor[rgb]{0,0,1}{\underline{-5x)}}\\
&0&+6x&-6\\
&&\textcolor[rgb]{0,1,0}{\underline{-(6x}}&\textcolor[rgb]{0,1,0}{\underline{-6)}}\\
&&0&+0
\end{array}$$

division in latex code:

\begin{array}{rlllr}

( x^3&+4x^2&+x& -6)&:(x-1)=\textcolor[rgb]{1,0,0}{x^2}\textcolor[rgb]{0,0,1}{+5x}\textcolor[rgb]{0,1,0}{+6}\\

\textcolor[rgb]{1,0,0}{{\underline{-(x^3}}&\textcolor[rgb]{1,0,0}{\underline{-x^2)}}}&&&\\

0&+5x^2&+x\\

&\textcolor[rgb]{0,0,1}{\underline{-(5x^2}}&\textcolor[rgb]{0,0,1}{\underline{-5x)}}\\

&0&+6x&-6\\

&&\textcolor[rgb]{0,1,0}{\underline{-(6x}}&\textcolor[rgb]{0,1,0}{\underline{-6)}}\\

&&0&+0

\end{array}

-----------------------

Many Greetings

Heureka (Eureka)

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

This is another possibility for long division

http://web2.0calc.com/questions/how-do-u-do-92-divide-6-3-in-long-division-nbsp

$$\;1\textcolor[rgb]{0,1,0}{4}\\
63|\bar{9}\bar{2}\bar{0} \qquad $63 goes into 92 just once$\\
'\;\;\;63\downarrow \qquad\; 1*63=63\\
'\;\;\;290\_\qquad\quad 92-63=29 \qquad $and bring down the 0$\\
'\;\;\;252\qquad\quad \textcolor[rgb]{0,1,0}{\mbox{63 goes into 290 4 times and 4*63=252}}\\
'\;\;\;\;\bar{3}\bar{8}\qquad \quad 290-252=38 $ The remainder is 36$$$

Coding is very messy though

\;1\textcolor[rgb]{0,1,0}{4}\\ 63|\bar{9}\bar{2}\bar{0} \qquad $63 goes into 92 just once$\\ '\;\;\;63\downarrow \qquad\; 1*63=63\\

'\;\;\;290\_\qquad\quad 92-63=29 \qquad $and bring down the 0$\\

'\;\;\;252\qquad\quad \textcolor[rgb]{0,1,0}{\mbox{63 goes into 290 4 times and 4*63=252}}\\ '\;\;\;\;\bar{3}\bar{8}\qquad \quad 290-252=38 $ The remainder is 36$

Hi Heureka,

I pasted your code (in the above post) into Texmaker at home and it will not run.  I want to play with it.  I thought it may need the $ signs around it but that didn't help.  Have you got any ideas on how i can get it to run.  I am not very good at deciphering the error messages.  I can past in the errors if it would help.

any ideas?

Thank you.

More great Latex from Heureka.  Thanks.

$$\\\left(0.084\;\frac{kg}{
\textcolor[rgb]{1,0,0}{\not}{w}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{k}
}\right)* \left( \frac{1\;
\textcolor[rgb]{1,0,0}{\not}{w}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{k}
}{7\;days} \right)=\frac{0.084}{7}\frac{kg}{days}=0.012\;\frac{kg}{days}\\\\
\Rightarrow 0.012\;\mbox{kg per day}$$

\\\left(0.084\;\frac{kg}{
\textcolor[rgb]{1,0,0}{\not}{w}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{k}
}\right)* \left( \frac{1\;
\textcolor[rgb]{1,0,0}{\not}{w}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{e}\textcolor[rgb]{1,0,0}{\not}{k}
}{7\;days} \right)=\frac{0.084}{7}\frac{kg}{days}=0.012\;\frac{kg}{days}\\\\
\Rightarrow  0.012\;\mbox{kg per day}

http://web2.0calc.com/questions/need-helppp-please-answer

I had to add a couple of preamble lines to get it to work in Texmaker.

\usepackage{pgfplots}

\pgfplotsset{compat=1.10}

$$\\\left(
\frac
{
1\;glass\
}
{
\frac{1}{8}\;\textcolor[rgb]{1,0,0}{\not}l
}
\right)*
\left( \frac{2.5\;
\textcolor[rgb]{1,0,0}{\not}{l}
}
{1\;bottle} \right)=2.5*8\;\frac{glass}{bottle}=20\;\frac{glass}{bottle}\\\\
\Rightarrow 20\;\mbox{glass per one bottle}$$

\\\left(
\frac
{
1\;glass\
}
{
\frac{1}{8}\;\textcolor[rgb]{1,0,0}{\not}l
}
\right)*
\left( \frac{2.5\;
\textcolor[rgb]{1,0,0}{\not}{l} 
}
{1\;bottle} \right)=2.5*8\;\frac{glass}{bottle}=20\;\frac{glass}{bottle}\\\\
\Rightarrow  20\;\mbox{glass per one bottle}

By Heureka

More Latex by Heureka:    

http://web2.0calc.com/questions/fractions_73#r106327

TexMaker  (Needed to add to make it work Both go in the preamble)

\usepackage{pgfplots}

\pgfplotsset{compat=1.10}

\theta= \tan^{-1}{(\frac{\Delta{y}}{\Delta{x}})} =

$$\theta= \tan^{-1}{(\frac{\Delta{y}}{\Delta{x}})} =$$

By Heureka.

\begin{array}{rll} 2x-8&=&6-5x\\ 7x&=&14\\ x&=&2 \end{array}

$$\begin{array}{rll}

2x-8&=&6-5x\\
7x&=&14\\
x&=&2
\end{array}$$

Top to botton Probability Tree (by Heureka)

http://web2.0calc.com/questions/if-you-flip-a-fair-coin-nbsp-4-nbsp-times-what-is-the-probability-that-you-will-get-exactly-nbsp-2-nbsp-tails#r5

Matrices (Heurika) 

http://web2.0calc.com/questions/quadratic-formula_6#r2

$$\[ \left( \begin{array}{cc}
1 & 2 \\
3 & 4
\end{array} \right)
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)
\]
\[ \left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)+
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 12 \\
1 & 18
\end{array} \right)
\]$$

\[ \left( \begin{array}{cc}
1 & 2 \\
3 & 4
\end{array} \right)
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)
\]
\[ \left( \begin{array}{cc}
0 & 6 \\
2 & 18
\end{array} \right)+
%
\left( \begin{array}{cc}
2 & 6 \\
-1 & 0
\end{array} \right)=
%
\left( \begin{array}{cc}
0 & 12 \\
1 & 18
\end{array} \right)
\]

 By Heureka

       $$\boxed{\begin{array}{lrcrcrr} (1) &5x & - & 14 &=& a &\\(2)& 2x& + & 1 &=& a &\\&--&-&--&-&--&\\(1) - (2)& 3x&-&15&=&0 & \quad | \quad :3\\&x&-&5&=&0 & \quad | \quad +5\\&\textcolor[rgb]{1,0,0}{x}&&&\textcolor[rgb]{1,0,0}{=}&\textcolor[rgb]{1,0,0}{5} &\end{array}}$$

\boxed{\begin{array}{lrcrcrr} (1) &5x & - & 14 &=& a &\\(2)& 2x& + & 1 &=& a &\\&--&-&--&-&--&\\(1) - (2)& 3x&-&15&=&0 & \quad | \quad :3\\&x&-&5&=&0 & \quad | \quad +5\\&\textcolor[rgb]{1,0,0}{x}&&&\textcolor[rgb]{1,0,0}{=}&\textcolor[rgb]{1,0,0}{5} &\end{array}}

(This one is cutesy of Reinout-g)

\begin{array}{|l|l|}32\% & 100\%\\0.32 & 1.00\\43.7 & 136.5625\\\end{array}   

$$\begin{array}{|l|l|}32\% & 100\%\\0.32 & 1.00\\43.7 & 136.5625\\\end{array}$$

Another from Heureka.  Thank you

http://web2.0calc.com/questions/5x-8-3x-3-whats-the-x

\underbrace{5x-3x}_{2x}-8=\underbrace{3x-3x}_0+3

$$\underbrace{5x-3x}_{2x}-8=\underbrace{3x-3x}_0+3$$

\begin{tabular}{|c|c|c|c|c|c|}

\hline
$x$&1&2&3&4&5\\\hline
$f(x)$&2&10&30&68&\\\hline

$$\begin{tabular}{|c|c|c|c|c|c|}

\hline
$x$&1&2&3&4&5\\\hline
$f(x)$&2&10&30&68&\\\hline
\end{tabular}$$

I am confused. What is @@LaTex

Melody, how do I write a graph so I can write it in an answer or a question with @@LaTex?

LaTex is a program for writing mathematical things.  It is what we use for all the presentations shown above.

If you would like to start learning you can start a new thread in the main part of the forum asking for some beginner lessons.  Please don't post in here any more because this thread is just for Latex reference not for learning with member help if that makes sense.

If anyone is really serious about learning, here is a good place to start

https://www.youtube.com/playlist?list=PLTejunv6WZfG-b9a0o0OcVMRpIJIlcHhF

This is where i got all my initial knowledge.  Alan started here too.

This message was sent to me by NinjaDevo via private message.

I am copying it here because it will probably be of interest to other people as well.

NINJA'S QUESTION:

I was looking through those LaTeX videos you posted in the LaTeX thread. 
I was wondering though, what's the difference between beginning a document and an array? For example, I see in some of your posts you did "\begin{array}{rll}" What does this mean and what does the rll mean in the brackets? 

Thanks, 
~Ninja 

MELODY'S ANSWER:

There a many different versions of LaTex which is really annoying. I am still glad I started with the videos, although i have actually not studied all of them. I should, it would probably help a lot.

When you write in Texmaker you have to enter the whole program, there are shortcuts to help you but you can still still see the whole thing. On any maths forum it is different. Some of it is pre-written so that you do not need to enter lines such as \begin{document} They have already been entered for you.

array is the term used when you want to line up objects such as equal signs.  There are a number of different types of arrays but this forum only seems to have the one.  It does everything the others do it is just a little harder to use and to be honest i haven't totally worked it out yet.

If i was going to wrtite a standard equation with the equal signs lined up then I woudl use 

I have added a litle equation solution to show you how it works

\begin{array}{rll}   note this must be ended with     

x-6&=&12\\

x&=&18

\end{array}    or it will not work!

Now array means you are lining things up.  r stands for right, l for left and c for centre.

The equal signs are going to line up.

The first input is going to be right aligned against the first&

The equal sign is pushed left so it butts up against the invisable first&

Then the other side of the equation is pushed left as well to butt up against the second &

There is always one more alignment command (l,r, or c) than the number of ampersands & used.

Now let's see if my code works.

$$\begin{array}{rll}
x-6&=&12\\
x&=&18
\end{array}$$

Good it worked well.     

Does that help Ninja?

Wow! That actually helped alot!

Thanks Melody. :)

31/7/14

Learning Latex Thread for beginners

http://web2.0calc.com/questions/here-is-a-question-just-for-latex-beginners-like-draagonslayer#r1

----------------------------------------------------------------------------------

What does this mean

\begin{array}{*{20}c}    Heureka answers here

http://web2.0calc.com/questions/here-is-a-question-just-for-latex-beginners-like-draagonslayer#r17

I found a list of LaTeX symbols with the command for them.

http://latex.wikia.com/wiki/List_of_LaTeX_symbols

This may be usefull to bookmark or refer back to.

I've just added the wiki referrnce address to the LaTex thread.

Thanks Ninja.

I did it Melody.

I will do it again.

$$6\frac{3}{4}$$

See Melody, I am really smart.

LOL

Hey guys,

I had another question about LaTeX. 
How do you put a single space between words in LaTeX? I know you can do /quad to put 4 spaces between text in LaTeX, but is there a way to put just one space, like when writing a sentence? 

Hi Ninja, my knowledge is not great - this is about all that I know 

SPACING

67

6\;7

6\:7

6\quad7

6\qquad7

-----------------------------

$$\\67\\
6\:7\\
6\;7\\
6\quad7\\
6\qquad7\\$$

Here is another 'learning LaTex' page from today.

http://web2.0calc.com/questions/3y-5x-13

Bold display

$$\mathbf{9.6*10^{14}}$$

\mathbf{9.6*10^{14}}

-------------------------------------------------

More LaTex display discussion.  Using $$ to turn off math mode

http://web2.0calc.com/questions/5-6-8-9

Hello, everyone. I have 2 questions.

Question 1) I really need to know how to make a graph in @@LaTex, but I can't figure out how to make one. Can somebody help me out please?

Question 2) Why do I have to use $$, \begindocument, and \enddocument in @@LaTex? Please help me. Thanks.

Lesson in Latex. Going in and out of math mode.         (9/8/14)

http://web2.0calc.com/questions/peter-has-12-marbles-he-gives-3-to-tom-and-5-to-lily-how-many-does-marbled-does-he-have-left#r2

Sorry Dragon I didn't see your last post when I posted mine - Does that make sense?

Question 1) I really need to know how to make a graph in @@LaTex, but I can't figure out how to make one. Can somebody help me out please?

I don't think that you can - you can make a table but not a graph.  What did you want to graph and I will tell you how we would do it?

Question 2) Why do I have to use $$, \begindocument, and \enddocument in @@LaTex? Please help me. Thanks.

I explained $$ in my last post.  It allows you to escape maths mode which is the default mode for the forum.  Look at my last post there is a lot more info there.

You do not need to use \begin{document} or \end{document} in the forum.

I think that you may have seen Alan use this? Alan writes his LaTex on his own computer in a program that he downloaded called Texmaker.  This is where we both learned LaTex.  He then copies the whole thing straight onto the forum.  If you use Texmaker then you have to enter begin document etc or it won't work.  In the forum that has already been done for you.  So I think that these lines do nothing at all when you use LaTex in the forum.

There does that answer your excellent questions Dragon?

Well, yes. I meant table. 

So, how do I make a table in @@LaTex?

(I always make a mistake when I say graph instead of table)

Look in the LaTex thread.  I'm pretty sure you will find the information that you need in there. 

Sorry - you are already in the LaTex thread.

Try this post.

http://web2.0calc.com/questions/latex#r21

Please show how to do summation symbol as i tried and it is not the same as elsewhere. Thanks. Also please say if $$ is input as dollar signs or backslashes and its puoose

Thanks Melody.

So, I just copy everything but I just cange a little things?

How to draw an answer box in LaTex. Or any box for that matter.

\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}}        $$\fbox{\begin{minipage}{0.6cm}\hfill\vspace{0.6cm}\end{minipage}}$$

-------------------------------------------------------------------------------------------

LaTex  Dragon's question also answers Stu's question.

 Question 2) Why do I have to use $$, \begindocument, and \enddocument in @@LaTex? Please help me. Thanks.

 You do not need to use any of this dragon.  Not in this forum anyway.

 Alan and I do use $$ sometimes.

 When writing in Latex you can be in maths mode or in non-maths mode.

 In this forum the default mode is maths mode.  If you do not want this you can cancel it at the very beginning of your program by entering $$  However, you do not need to do this.  You can just work in maths mode which is what most people do.

 This symbol \ is called a backslash

\\ means start a new line.  This is not done automatically you have to 'tell the code to do it' with this command.

 One \ indicates a function is coming.  Sometimes functions have 1 or more 'arguaments' these must be put in parentheses { }

 like \frac{1}{2} or \sqrt{49} or \quad

 If you want to display a $ sign you need to put \$ because $ is a reserved key and so this will symolise that it is ONLY the symbol itself that you want.

 Now Dragon.  Yes if you want to do something that has been demonstrated.  Just copy the code and change little things.  You will slowly gain understanding about what everything means.

 I hope that all this information helps.  

Yes. It helps. But do I change the x and y part?

Dragon - What x and y part?

also can you continue this in a new thread on the forum please.

This thread is intended more for information - not so much for questions.  

You can giveyour new thread a title something like LaTex help 

If you want to refer to something that I have written here maybe you could copy it over so I know what you are talking about.   

I mean this.

\begin{tabular}{|c|c|c|c|c|c|}

\hline
$x$&1&2&3&4&5\\\hline
$f(x)$&2&10&30&68&\\\hline

So, can I make a Thread that says, @@LaTex Questions?

I posted the answer and I am waiting.

Yes fine dragon.  I only just saw this.

You can ask questions on the forum, that is what it is for.

I don't know that you have enough knowledge yet to answer other people's LaTex. (But you are welcome to try)

I think you should concentrate on improving your own LaTex first.   

Try my best, I will. But help others, is later.

$$\begin{tabular}{cccccc}
&&\;x^2&-11&+28&
&&&||&||&||&||&
x&-2&\|\;x^3&-13x^2&+50x&-56\\
&&\;x^3&-2x^2&&&
&&||&||&||&||&
&&&-11x^2&+50x&-56&\\
&&&-11x^2&+22x&&
&&&||&||&||&
&&&&+28x&-56&\\
&&&&+28x&-56&
&&&&||&||&
&&&&&0&
\end{tabular}$$

\begin{tabular}{cccccc} &&\;x^2&-11&+28& &&&||&||&||&||& x&-2&\|\;x^3&-13x^2&+50x&-56\\ &&\;x^3&-2x^2&&& &&||&||&||&||& &&&-11x^2&+50x&-56&\\ &&&-11x^2&+22x&& &&&||&||&||& &&&&+28x&-56&\\ &&&&+28x&-56& &&&&||&||& &&&&&0& \end{tabular}

I found out that the dollar sign is \.

How to do Latex Coding's

Hi Selena, 

you learn by copying - justr little things at first like making a fraction.  there is lots of code that you can play with in this thread.   :)

Ok kcool an hey XD

Do you guys actually type all the letters?

Sometimes I copy them from here and paste them in but mostly i type them all.  :)

I usually work the problems out and code them straight in at the same time.

I often refer back to this thread to get the more complicated code that I want to use. 

This thread could really use cleaning up but for the moment it works for me. :)

I am not sue how many other people use it - not many I think.

LaTex is cool.  It is fun to learn, fun to use, and it makes the answers (and questions) easier to read and easier to interprete. 

Heueka just wrtote some electricity formulas with LaTex - a few new symbols I think.  Thanks Heureka.

http://web2.0calc.com/questions/if-voltage-source-is-12-resistance-is-6800-and-voltage-1-is-8-what-is-r2#r1

Another of Heureka's masterpeices.   (26/1/15)

$$\left[\ 1+\frac{1}{3}+\frac{2}{3}+\frac{2}{9}+\frac{4}{9}+\frac{4}{27}+\frac{8}{27} +\frac{8}{81} +\frac{16}{81}+\dots \ \right] \\\\ \\= 1+ \frac{1}{3} + \frac{2}{3} + \underbrace{\frac{1}{3}*\frac{2}{3} }_{=\frac{2}{9}}+ \underbrace{\frac{2}{3}*\frac{2}{3} }_{=\frac{4}{9}}+ \underbrace{\frac{1}{3}*\frac{4}{3^2} }_{=\frac{4}{27}}+ \underbrace{\frac{2}{3}*\frac{4}{3^2} }_{=\frac{8}{27}}+ \underbrace{ \frac{1}{3}* \frac{8}{3^3}}_{=\frac{8}{81}}+ \underbrace{\frac{2}{3}*\frac{8}{3^3}}_{=\frac{16}{81}}+\dots \ \\\\\\= 1+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{2}{3}}+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{4}{3^2}}+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{8}{3^3}}+\dots \ \\\\\\= 1+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{2}{3}}+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{2^2}{3^2}}+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{2^3}{3^3}}+\dots \ \\\\\\= 1+ 1+ \frac{2}{3}}+ \frac{2^2}{3^2}}+ \frac{2^3}{3^3}}+\dots \ \\\\\\s=1+1*( \frac{2}{3} ) ^0+1*(\frac{2}{3})^1+1*(\frac{2}{3})^2+1*(\frac{2}{3})^3+1*(\frac{2}{3})^4+\dots \$$

\left[\ 1+\frac{1}{3}+\frac{2}{3}+\frac{2}{9}+\frac{4}{9}+\frac{4}{27}+\frac{8}{27} +\frac{8}{81} +\frac{16}{81}+\dots \ \right] \\\\\\

= 1+ \frac{1}{3} + \frac{2}{3} + \underbrace{\frac{1}{3}*\frac{2}{3} }_{=\frac{2}{9}}+ \underbrace{\frac{2}{3}*\frac{2}{3} }_{=\frac{4}{9}}+ \underbrace{\frac{1}{3}*\frac{4}{3^2} }_{=\frac{4}{27}}+ \underbrace{\frac{2}{3}*\frac{4}{3^2} }_{=\frac{8}{27}}+ \underbrace{ \frac{1}{3}* \frac{8}{3^3}}_{=\frac{8}{81}}+ \underbrace{\frac{2}{3}*\frac{8}{3^3}}_{=\frac{16}{81}}+\dots \ \\\\\\

= 1+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{2}{3}}+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{4}{3^2}}+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{8}{3^3}}+\dots \ \\\\\\

= 1+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{2}{3}}+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{2^2}{3^2}}+ ( \underbrace{\frac{1}{3} + \frac{2}{3} }_{=1} )*\frac{2^3}{3^3}}+\dots \ \\\\\\

= 1+ 1+ \frac{2}{3}}+ \frac{2^2}{3^2}}+ \frac{2^3}{3^3}}+\dots \ \\\\\\s=1+1*( \frac{2}{3} ) ^0+1*(\frac{2}{3})^1+1*(\frac{2}{3})^2+1*(\frac{2}{3})^3+1*(\frac{2}{3})^4+\dots \

Using Vectors

\vec{V_1}

$$\vec{v_1}$$

Binomials

\displaystyle\binom{5}{i}

$$\displaystyle\binom{5}{i}$$

\displaystyle \sum \limits_{i=0}^{\textcolor[rgb]{1,0,0}{5-1}} *(-1)^i*\binom{5}{i}* (5-i)^3 \hspace {15}| \hspace {15} \Text {N=5 \; k=3} \\\

$$\displaystyle \sum \limits_{i=0}^{\textcolor[rgb]{1,0,0}{5-1}} *(-1)^i*\binom{5}{i}* (5-i)^3 \hspace{15pt}| \hspace{15pt} \Text {N=5 \; k=3} \\\$$

Partial Derivatives

\dfrac{\partial z}{\partial x}

$$\dfrac{\partial z}{\partial x} =0.3x^{-0.7}y^{0.5}$$

I want to learn this!

Good MG

I want you to learn it too :)

Nauseated's code

http://web2.0calc.com/questions/a-3-2-5-x-b-10-2-c-20-d-10#r4

Some of it isn't working properly (it did fro Nauseated)  - I have changed some of it a bit but it didn't all work to start with and it still doesn't now!  NEEDS WORK

$$\Displaystyle \text {Basic form} \\\Displaystyle x^{3^4}\\ \Displaystyle \text {This format will work for more complex forms}\\\Displaystyle \begin{Large} {X^{2^4^{^6^}^{^8^}^{^{Etc}}}\end{Large}\\\\\text {Here are some other presentation forms that may be useful.}\\$$

$$\Displaystyle \text {Basic form} \\\Displaystyle x^{3^4}\\ \Displaystyle \text {This format will work for more complex forms}\\\Displaystyle \begin{Large} {X^{2^4^{^6^}^{^8^}^{^{Etc}}}\end{Large}\\\\\text {Here are some other presentation forms that may be useful.}\\$$

------------------------------------------------

\Displaystyle \text {Basic form} \\\Displaystyle x^{3^4}\\

\Displaystyle \text {This format will work for more complex forms}\\

\Displaystyle \begin{Large} {X^{2^4^{^6^}^{^8^}^{^{Etc}}}\end{Large}\\\\

\text {Here are some other presentation forms that may be useful.}\\ 

------------------------------------------------

$$\noindent \sqrt[\leftroot{-2}\uproot{4} 7]9876 \leftarrow \Text${Use noindent to prevent pesky indentation}\\\\$$

\noindent \sqrt[\leftroot{-2}\uproot{4} 7]9876 \leftarrow \Text${Use noindent to prevent pesky indentation}\\\\

$$noindent \sqrt[\leftroot{-2}\uproot{4} 7]{9876}\leftarrow \Text${Note the root function covers all the numbers here. Compare the codes to see why} \\\\$$

noindent \sqrt[\leftroot{-2}\uproot{4} 7]{9876}\leftarrow \Text${Note the root function covers all the numbers here. Compare the codes to see why} \\\\

\Text{Here's a method to nest "n-root" and align the "n" using "leftroot" and "uproot"}\\\\\

$$\sqrt[\leftroot{-2}\uproot{4} 7]{\sqrt[\leftroot{-2}\uproot{4} 5]{ (\sqrt[\leftroot{-2}\uproot{2} 9]{x^2})^3}} = Z \\\\
\Text{Note the subtle difference in the exponent of 3}\\\\$$

\sqrt[\leftroot{-2}\uproot{4} 7]{\sqrt[\leftroot{-2}\uproot{4} 5]{ (\sqrt[\leftroot{-2}\uproot{2} 9]{x^2})^3}} = Z \\\\

\Text{Note the subtle difference in the exponent of 3}\\\

\sqrt[\leftroot{-2}\uproot{4} 7]{\sqrt[\leftroot{-2}\uproot{4} 5]{ (\sqrt[\leftroot{-2}\uproot{2} 9]{x^2})^{^3}}} = Z \\\ \Text{One great thing about writing great LaTex presentations: You can be dumber than a box of rocks and still look intelligent --at least for awhile. I have been getting away with it for years . . . .} 

Hi Nauseated,

I want to compare some of what you have done to how I would do it.

NAUSEATED'S    CODE

$$\noindent \sqrt[\leftroot{-2}\uproot{4} 7]9876 \leftarrow \Text${Use noindent to prevent pesky indentation}\\\\$$

\noindent \sqrt[\leftroot{-2}\uproot{4} 7]9876 \leftarrow \Text${Use noindent to prevent pesky indentation}\\\\

$$\noindent \sqrt[\leftroot{-2}\uproot{4} 7]{9876}\leftarrow \Text${Note the root function covers all the numbers here. Compare the codes to see why} \\\\$$

noindent \sqrt[\leftroot{-2}\uproot{4} 7]{9876}\leftarrow \Text${Note the root function covers all the numbers here. Compare the codes to see why} \\\\

MELODY'S  CODE

$$\\\sqrt[7]{9876}\leftarrow $No indent because of the 2 backslashes $$$

\\\sqrt[7]{9876}\leftarrow $No indent because of the 2 backslashes $

If I  wanted just the 9 under the square root I would  only put the 9 in the parentheses

Note: I have never seen Text${...   }  used before.  I either use $...   $   

which Alan discovered,   OR I use   \mbox{....} 

It is good to know of alternatives because sometimes they work better under different circumstances. :)

------------------------------------------

NAUSEATED'S  CODE

$$\Displaystyle \text {Basic form} \\\Displaystyle x^{3^4}\\
\Displaystyle \text {This format will work for more complex forms}\\
\Displaystyle \begin{Large} {X^{2^4^{^6^}^{^8^}^{^{Etc}}}\end{Large}\\\\
\text {Here are some other presentation forms that may be useful.}\\$$

\Displaystyle \text {Basic form} \\\Displaystyle x^{3^4}\\

\Displaystyle \text {This format will work for more complex forms}\\

\Displaystyle \begin{Large} {X^{2^4^{^6^}^{^8^}^{^{Etc}}}\end{Large}\\\\

\text {Here are some other presentation forms that may be useful.}\\ 

This last one is of great interest to me.  Thanks Nauseated :)

-------------------------------------------------

$$\sqrt[\leftroot{-2}\uproot{4} 7]{\sqrt[\leftroot{-2}\uproot{4} 5]{ (\sqrt[\leftroot{-2}\uproot{2} 9]{x^2})^3}} = Z \\\\
\Text${Note the subtle difference in the exponent of 3}\\\
\sqrt[\leftroot{-2}\uproot{4} 7]{\sqrt[\leftroot{-2}\uproot{4} 5]{ (\sqrt[\leftroot{-2}\uproot{2} 9]{x^2})^{^3}}} = Z \\\$$

\sqrt[\leftroot{-2}\uproot{4} 7]{\sqrt[\leftroot{-2}\uproot{4} 5]{ (\sqrt[\leftroot{-2}\uproot{2} 9]{x^2})^3}} = Z \\\\          

NOTE: for this one the 3 is the same height as the 2. 

\Text${Note the subtle difference in the exponent of 3}\\\

\sqrt[\leftroot{-2}\uproot{4} 7]{\sqrt[\leftroot{-2}\uproot{4} 5]{ (\sqrt[\leftroot{-2}\uproot{2} 9]{x^2})^{^3}}} = Z \\\    

NOTE: for this one the 3 is higher than the 2

Nauseated - I have a question.  You seem to use 2 backslashes quite often and I am wondering why.

2 will give you a new line and 1 usually gives me a $ sign but this does not seem to be happening for you.

So I am a bit confused. 

WHY IS MY LATEX NOT DISLPLAYING - SOMETIMES IT DOES - SOMETIMES IT DOESN'T.

IT IS FINE WHILE I WORK ON THE POST THEN THE FINISHED POST SOMETIMES DOES NOT DISPLAY PROPERLY.

WEIRD!!!

A nice table drawn by Heureka :)

\small{\begin{array}{c|c}\text{nat\"urliche Zahl} & \text{Dreierpotenz} \\

\hline\\(0) & 0^3 \\1 & 1^3 \\2 & 2^3 \\3 & 3^3 \\4 & 4^3 \\5 & 5^3 \\\cdots & \cdots \\n & n^3 \\\\\hline\end{array}}

$$\small{\begin{array}{c|c}\text{nat\"urliche Zahl} & \text{Dreierpotenz} \\
\hline\\(0) & 0^3 \\1 & 1^3 \\2 & 2^3 \\3 & 3^3 \\4 & 4^3 \\5 & 5^3 \\\cdots & \cdots \\n & n^3 \\\\\hline\end{array}}$$

This is an inital learning thread for LaTex.       Thanks MathsGod1 for initiating it :)

http://web2.0calc.com/questions/latex-form

MG I whited out some of the other bits that you put here.  I want it to stay an information thread.

I know it is very messy by I still reference it constantly.  

I am thinking that if you get good at LaTex maybe one day you will clean this thread up for us and we will have a nice neat new thread :)

By the way, LaTex is pronounced    Lay Tec

Different \dot commands.

Heureka has given us a display of them - there is a lot.     Thanks Heureka

http://web2.0calc.com/questions/algebra_545#r4

Vector and Matrix coding by Heureka      (7/5/15)

http://web2.0calc.com/questions/if-three-points-of-a-parallelogram-are-located-at-1-0-4-3-and-5-2-what-is-the-fourth-coordinate#r4

 This is Heureka's coding      

 from here

http://web2.0calc.com/questions/in-the-figure-below-ab-ac-50-ad-52-nbsp-and-bc-28-nbsp-determine-cd#r5

$$\small{\text{$\begin{array}{l|l}A=\sqrt{s\cdot (s-a)\cdot(s-b)\cdot (s-c)} & \qquad \overline{AB} = a=50, ~ \overline{AC} = b=50,~ \overline{AD} =c=28\\\\& \qquad s = \frac{a+b+c}{2}=\frac{50+50+28}{2}=\frac{128}{2}=64 \\A=\sqrt{s\cdot (s-50)\cdot(s-50)\cdot (s-28)} \\A= \sqrt{64\cdot (64-50)\cdot(64-50)\cdot (64-28)} \\ A= \sqrt{64\cdot 14 \cdot 14 \cdot 36} \\A= \sqrt{8^2\cdot 14^2 \cdot 6^2} \\ A= 8\cdot 14 \cdot 6 \\ A=672\end{array}$}}$$

\small{\text{$\begin{array}{l|l}A=\sqrt{s\cdot (s-a)\cdot(s-b)\cdot (s-c)} & \qquad \overline{AB} = a=50, ~ \overline{AC} = b=50,~ \overline{AD} =c=28\\\\

& \qquad s = \frac{a+b+c}{2}=\frac{50+50+28}{2}=\frac{128}{2}=64 \\

A=\sqrt{s\cdot (s-50)\cdot(s-50)\cdot (s-28)} \\

A= \sqrt{64\cdot (64-50)\cdot(64-50)\cdot (64-28)} \\

A= \sqrt{64\cdot 14 \cdot 14 \cdot 36} \\

A= \sqrt{8^2\cdot 14^2 \cdot 6^2} \\

A= 8\cdot 14 \cdot 6 \\

A=672\end{array}$}}

-------------------------------

What is  \text{$   for?   What does it do, I see no text.

big         \small{mathe-Modus}}     :             $$\small{mathe-Modus}}$$

small      \small{\text{text-Modus}} :            $$\small{\text{text-Modus}}$$

small - italic    \small{\text{$mathe-Modus-italic$}} :     $$\small{\text{$mathe-Modus-italic$}}$$

BOXES FROM NAUSEATED      18/5/15

Original         http://web2.0calc.com/questions/latex-form-part-2#r52

\setlength{\fboxsep}{20pt}\fbox{Hi Melody. Here are a few ways to do "quick" boxes} \\\\

$$\setlength{\fboxsep}{20pt}\fbox{Hi Melody. Here are a few ways to do "quick" boxes} \\\\$$

\setlength{\fboxsep}{20pt}\fbox{} \\\\

\setlength{\fboxsep}{15pt}\fbox{} \\\\

$$\setlength{\fboxsep}{20pt}\fbox{}\\\\
setlength{\fboxsep}{15pt}\fbox{} \\\\$$

\setlength{\fboxsep}{10pt}\fbox{} \\\\

setlength{\fboxsep}{5pt}\fbox{} \\\\

$$\setlength{\fboxsep}{10pt}\fbox{} \\\\
setlength{\fboxsep}{5pt}\fbox{} \\\\$$

\setlength{\fboxsep}{20pt} \fbox{ } \leftarrow ${Comds are the same, except for} \\\\

$$\setlength{\fboxsep}{20pt} \fbox{ } \leftarrow ${Comds are the same, except for} \\\\$$

\setlength{\fboxsep}{15pt}\fbox{ } \leftarrow ${ one space for additional [x]pt width}

$$\setlength{\fboxsep}{15pt}\fbox{ } \leftarrow ${ one space for additional [x]pt width}$$

\setlength{\fboxsep}{10pt}\fbox{ } \\\\

setlength{\fboxsep}{5pt}\fbox{ } \\\\

$$\setlength{\fboxsep}{10pt}\fbox{ } \\\\
setlength{\fboxsep}{5pt}\fbox{ } \\\\$$

\setlength{\fboxrule}{3pt}\setlength{\fboxsep}{6pt} \fbox{ } \leftarrow ${ fboxrule Comds affect border boldness}\\\\

$$\setlength{\fboxrule}{3pt}\setlength{\fboxsep}{6pt} \fbox{ } \leftarrow ${ fboxrule Comds affect border boldness}\\\\$$

\setlength{\fboxrule}{5pt}\setlength{\fboxsep}{15pt} \fbox{? } \leftarrow ${ Text (if used) is Center justified } \\\\

$$\setlength{\fboxrule}{5pt}\setlength{\fboxsep}{15pt} \fbox{? } \leftarrow ${ Text (if used) is Center justified } \\\\$$

\setlength{\fboxrule}{3pt}\setlength{\fboxsep}{15pt} \fbox{ End of Examples from }

$$\setlength{\fboxrule}{3pt}\setlength{\fboxsep}{15pt} \fbox{ End of Examples from }$$

\setlength{\fboxrule}{5pt}\setlength{\fboxsep}{20pt} \fbox{ Your friendly neighborhood Troll }

$$\setlength{\fboxrule}{5pt}\setlength{\fboxsep}{20pt} \fbox{ Your friendly neighborhood Troll }$$

-------------------------------------------------------------------------------------------------------------

$$\setlength{\fboxsep}{20pt}\fbox{Hi Melody. Here are a few ways to do "quick" boxes} \\\\
\setlength{\fboxsep}{20pt}\fbox{} \\\\
\setlength{\fboxsep}{15pt}\fbox{} \\\\
\setlength{\fboxsep}{10pt}\fbox{} \\\\
\setlength{\fboxsep}{5pt}\fbox{} \\\\
\setlength{\fboxsep}{20pt} \fbox{ } \leftarrow ${Comds are the same, except for} \\\\
\setlength{\fboxsep}{15pt}\fbox{ } \leftarrow ${ one space for additional [x]pt width} \setlength{\fboxsep}{10pt}\fbox{ } \\
\setlength{\fboxsep}{5pt}\fbox{ } \\\\
setlength{\fboxrule}{3pt}\setlength{\fboxsep}{6pt} \fbox{ } \leftarrow ${ fboxrule Comds affect border boldness}\\\\
\setlength{\fboxrule}{5pt}\setlength{\fboxsep}{15pt} \fbox{? } \leftarrow ${ Text (if used) is Center justified } \\\\
\setlength{\fboxrule}{3pt}\setlength{\fboxsep}{15pt} \fbox{ End of Examples from } \setlength{\fboxrule}{5pt}\setlength{\fboxsep}{20pt} \fbox{ Your friendly neighborhood Troll }$$

$$$
\root 3 \of {x \root 3 \of {x \root 3 \of {x \sqrt{x}}}}
$$$

this is made my latex:

$$$\LaTeX$$$

Heureka 3/8/15

http://web2.0calc.com/questions/how-come-30-99-61-100-is-divisible-by-31#r4

\small{\text{$30 \equiv - 1 \pmod {31}$}}\\

\small{\text{ and $61 \equiv - 1 \pmod {31}$}}\\\\

\small{\text{$(-1)^{99} + (-1)^{100} \stackrel{?}\equiv 0 \pmod{31}$}}\\\\

\small{\text{$-1 + 1 \equiv 0 \pmod{31}$}}\\\\

OUTPUT

$$\small{\text{$30 \equiv - 1 \pmod {31}$}}\\
\small{\text{ and $61 \equiv - 1 \pmod {31}$}}\\\\
\small{\text{$(-1)^{99} + (-1)^{100} \stackrel{?}\equiv 0 \pmod{31}$}}\\\\
\small{\text{$-1 + 1 \equiv 0 \pmod{31}$}}\\\\$$

------------------------------------------

\stackrel{?}\equiv

OUTPUT

$$\stackrel{?}\equiv$$

$$ \underbrace{a+\overbrace{b+\cdots}^{{}=t}+z} _{\mathrm{total}} ~~ a+{\overbrace{b+\cdots}}^{126}+z $$

LaTeX coding is FUN!

A great trig diagram from Heureka.                                 26th June 2016

http://web2.0calc.com/questions/sine-law_1

Thanks to MaxWong                                 Cards Suites  

A card is drawn at random from a pack of 52 playing cards(\(\clubsuit \diamondsuit \heartsuit \spadesuit\))

(without Jokers). What is the probability of getting a card which is neither a 6 nor a ?

\clubsuit \diamondsuit \heartsuit \spadesuit

More symbols here  :))   Thanks Max

http://web2.0calc.com/questions/off-topic-just-trying-to-make-a-picture

There are many really helpful symbols here

 http://omega.albany.edu:8008/Symbols.html

\dagger              \(\dagger   \)  

\S                    §

\infty               \(\infty   \)    

\cdot \space \cdot \\ \smile               \(\cdot \space \cdot \\ \smile          \)

\cdot \space \cdot \\ \frown             \(\cdot \space \cdot \\ \frown \)  

A page of Latex explanation contributed by MaxWong.  Thanks Max    

http://web2.0calc.com/questions/a-post-of-latex

Just discovered how to escape from Math mode of LaTeX while the above method won't work for me(The $ one)

\text{}

\(\text{2^5}\)\text{2^5}

\(\text{The above one have completely escaped from math mode, so is this one}\)

\text{The above one have completely escaped from math mode, so is this one}

\(\begin{align*}2x - 5y &= 8\\3x + 9y &= -12\end{align*}\)

Hey look Mom, I did align XDDDDD

This little gem is  Heureka's  -  thanks Heureka :)     

http://web2.0calc.com/questions/statistics_427#r2

\begin{array}{|lcll|} \hline \text{Set students } ~ s &=& 62 \\ \text{Set freshman } ~ f &=& 32 \\ \text{Set economics major} ~ e_m &=& 32 \\ \text{Set neither} ~ n &=& 12 \\\\ \text{both a freshman and economics major } &=& f+e_m+n -s \\ &=& 32+32+12-62 \\ &=& 14 \\\\ \text{the probablity is the student is both a freshman and economics major } &=& \frac{f+e_m+n -s}{s} \\ &=& \frac{14}{62} \\ &=& \frac{7}{31} \quad ( 22.58\ \%)\\ \hline \end{array}

\(\begin{array}{|lcll|} \hline \text{Set students } ~ s &=& 62 \\ \text{Set freshman } ~ f &=& 32 \\ \text{Set economics major} ~ e_m &=& 32 \\ \text{Set neither} ~ n &=& 12 \\\\ \text{both a freshman and economics major } &=& f+e_m+n -s \\ &=& 32+32+12-62 \\ &=& 14 \\\\ \text{the probablity is the student is both a freshman and economics major } &=& \frac{f+e_m+n -s}{s} \\ &=& \frac{14}{62} \\ &=& \frac{7}{31} \quad ( 22.58\ \%)\\ \hline \end{array}\)

ALIGNING  FOR  EQUATIONS      (Thanks Heureka)

http://web2.0calc.com/questions/logarithm_26766#r5

\begin{array} {rcl}... &=&...\end{array}
left side:         r = right aligned
Second field:   c = center
right side:          l = left aligned

BINOMIALS

\binom30^2 + \binom31^2 + \binom32^2 + \binom33^2

\(\binom30^2 + \binom31^2 + \binom32^2 + \binom33^2\)

\binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 = \text{ something}.

\(\binom{n}{0}^2 + \binom{n}{1}^2 + \cdots + \binom{n}{n}^2 = \text{ something}.\)

----------------------------------------------------------------------------------------------------------

FRACTIONS

\cfrac   and    \dfrac

\cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{2 + \dotsb}}}}

\(\cfrac{1}{1 + \cfrac{1}{2 + \cfrac{1}{1 + \cfrac{1}{2 + \dotsb}}}}\)

More here

http://tex.stackexchange.com/questions/59747/proper-display-of-fractions

On that reference site there is also a \dfrac{}{} used.

2-\frac{2}{1-\left(\frac{2}{2-\frac{2}{x^2}}\right)}\quad

2-\dfrac{2}{1-\left(\dfrac{2}{2-\dfrac{2}{x^2}}\right)}\quad

2-\cfrac{2}{1-\left(\cfrac{2}{2-\cfrac{2}{x^2}}\right)}\quad

2-\dfrac{2}{1-\left(\cfrac{2}{2-\dfrac{2}{x^2}}\right)}

\(2-\frac{2}{1-\left(\frac{2}{2-\frac{2}{x^2}}\right)}\quad 2-\dfrac{2}{1-\left(\dfrac{2}{2-\dfrac{2}{x^2}}\right)}\quad 2-\cfrac{2}{1-\left(\cfrac{2}{2-\cfrac{2}{x^2}}\right)}\quad 2-\dfrac{2}{1-\left(\cfrac{2}{2-\dfrac{2}{x^2}}\right)}\)

Mmm,   I can't see the difference between the cfrac and the dfrac     :

*

How to put different types of brackets around matrices - or no brackets at all !

http://web2.0calc.com/questions/test-2#r2

http://www.sascha-frank.com/Faq/matrices.html

\text{This text } \begin{smallmatrix} 2\\ 3\\ \end{smallmatrix} \;\;\text{is only for showing.}

\(\text{This text } \begin{smallmatrix} 2\\ 3\\ \end{smallmatrix} \;\;\text{is only for showing.}\)

GingerAle's LaTex in a box

\begin{array}{|lll|} \hline &(h-16t^2) - (h-16(t+1.6)^2) &=& 182ft&\\

&-16t^2+16 (t+1.6)^2&=&182\\ &51.2t+40.96&=&182\\

&51.2t&=&141.04\\

&t&=&2.7546875\\ \text { }\\

&16(2.7546875)^2 &=& 121.4 \text{ft above observation floor. }\\

&\dfrac{121.4}{13}& =& 9.3 \text{ Floors above observation floor. }\\

&14+9 &=& 23 \text { The bucket fell from the }23^{rd} \text {floor }\\

\hline \end{array}

\(\begin{array}{|lll|} \hline &(h-16t^2) - (h-16(t+1.6)^2) &=& 182ft&\\ &-16t^2+16 (t+1.6)^2&=&182\\ &51.2t+40.96&=&182\\ &51.2t&=&141.04\\ &t&=&2.7546875\\ \text { }\\ &16(2.7546875)^2 &=& 121.4 \text{ft above observation floor. }\\ &\dfrac{121.4}{13}& =& 9.3 \text{ Floors above observation floor. }\\ &14+9 &=& 23 \text { The bucket fell from the }23^{rd} \text {floor }\\ \hline \end{array}\)

Why can't I see this in the sticky notes?