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day#03.tex
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day#03.tex
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%% Brackets, Tables and Arrays
\documentclass[11pt]{article}
\usepackage{amssymb, amsmath, amsfonts}
\usepackage{float}
\parindent 0px
\pagestyle{empty}
\begin{document}
$$::Brackets::$$\\[20pt]
The distributive property states that $a(b+c)=ab+ac$, for all $a, b, c \in \mathbb{R}$.\\[6pt]
The equivalence class of $a$ is $[a]$.\\[6pt]
The set $A$ is defined to be $\{1,2,3\}$.\\[6pt]
The movie ticket is $\$11.50$.
$$2\left(\frac{1}{x^2-1}\right)$$
$$2\left[\frac{1}{x^2-1}\right]$$
$$2\left\{\frac{1}{x^2-1}\right\}$$
Angular bracket
$$2\left \langle \frac{1}{x^2-1}\right \rangle $$
Absolute value symbol
$$2\left | \frac{1}{x^2-1}\right | $$
$$\left.\frac{dy}{dx}\right|_{x=1}$$
$$\left(\frac{1}{1+\left(\frac{1}{1+x}\right)}\right)$$
Tables:\\
\begin{tabular}{|c||c|c|c|c|c|}
% c means element position in center of the single box and the nuber of c is equal to the number of column of the table.
%% \begin{tabular}{llllll}
% l means element position in left of the single box and the nuber of l is equal to the number of column of the table.
%% \begin{tabular}{rrrrrr}
% r means element position in right of the single box and the nuber of r is equal to the number of column of the table.
%x 1 2 3 4 5
\hline
$x$ & 1 & 2 & 3 & 4 & 5 \\ \hline
$f(x)$ & 10 & 11 & 12 & 13 & 14 \\ \hline
\end{tabular}
\vspace{1cm}
\begin{table}[H]
\centering
\def \arraystretch{1.5}
\begin{tabular}{|c||c|c|c|c|c|}
\hline
$x$ & 1 & 2 & 3 & 4 & 5 \\ \hline
$f(x)$ & $\frac{1}{2}$ & 11 & 12 & 13 & 14 \\ \hline
\end{tabular}
\caption{These values represent the function of $f(x)$.}
\end{table}
\begin{table}[H]
\centering
\def \arraystretch{1.5}
\caption{The relationship between $f$ and $f'$.}
\begin{tabular}{|l|p{4in}|}
\hline
$f(x)$ & $f'(x)$ \\ \hline
$x>0$ & The function $f(x)$ if increasing.The function $f(x)$ if increasing.The function $f(x)$ if increasing.The function $f(x)$ if increasing.The function $f(x)$ if increasing. \\ \hline
\end{tabular}
\end{table}
Arrays::
% \, this is need when we want to use a space between two things
\begin{align}
5x^2\,\text{place your words here} \\
5x^2\text{ your words}\\
5x^2-9=x+3\\
5x^2-x-12=0
\end{align}
\begin{align*}
5x^2-9&=x+3\\
5x^2-x-12&=0\\
&=12-x-5x^2
\end{align*}
\begin{align}
5x^2-9&=x+3\\
5x^2-x-12&=0\\
&=12-x-5x^2
\end{align}
\end{document}