\documentclass[12pt]{amsart}
\begin{document}

\[
\int_a^b f(x)dx = \lim_{\Delta x\rightarrow 0} \sum_{i=1}^n f(x_i) \Delta x
\]

\par\vspace{1 cm}

\[
|x|=
\left\{
\begin{array}{rcl}
 x & \mbox{if} & x\geq 0 \\
-x & \mbox{if} & x<0    \\
\end{array}
\right.
\]

\par\vspace{1 cm}\noindent

We say that the limit of $f$ as $x$ approaches $a$ is $L$ and write 

\[
\lim_{x\rightarrow a} f(x)=L
\vspace{0.3 cm}
\] 

if, for every $\epsilon>0$, there exists a $\delta>0$ such that

\[
|f(x)-L|<\epsilon \mbox{ whenever } |x-a|<\delta
\]

\par\vspace{1 cm}\noindent

Define $f:\mathbb{R}\times\mathbb{R}\rightarrow\mathbb{R}$ by

\[
f(x,y)=\frac{1}{\sqrt{1+x^2+y^2}},\quad x,y\in\mathbb{R}
\]

\par\vspace{1 cm}\noindent

The truth table for $P\vee Q$ is:

\par\vspace{1 cm}

\begin{center}

\begin{tabular}{c|c|c}
$P$ & $Q$ & $P\vee Q$\\
\hline
T & T & T\\
T & F & T\\
F & T & T\\
F & F & F\\
\end{tabular}

\end{center}

\end{document}
