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\documentclass[twocolumn,a4paper,11pt]{article}
\usepackage{palatino}
\begin{document}
\title{Mathematical exercises}
\author{Now its up to you}
\date{Time to have fun}
\maketitle
Just do as many of these as you can.
\begin{equation}
(fg)'=f'g+fg'
\end{equation}
\begin{equation}
\alpha\beta=\gamma+\delta
\end{equation}
\begin{equation}
\Gamma(n)=(n-1)
\end{equation}
\begin{equation}
X\wedge(Y\vee Z)=
(X\wedge Y)\vee(X\wedge Z)
\end{equation}
\begin{equation}
2+4+6+...+2n=n(n+1)
\end{equation}
\begin{equation}
\vec{x}\cdot\vec{y}\not=0
\mbox{ if and only if }
\vec{x}\not\perp
\vec{y}
\end{equation}
\begin{equation}
(\forall x \epsilon\Re)
(\exists y\epsilon\Re)y >x
\end{equation}
\begin{equation}
\frac{a+b}{c}\quad
\frac{a}{b+c} \quad
\frac{1}{a+b+c}\not=
\frac{1}{a}+\frac{1}{b}+\frac{1}{c}
\end{equation}
\begin{equation}
e^x\quad e^{-x}\quad
e^{i\pi}+1=0\quad
x_0 \quad x^2_o \quad
x^{\;2}_o \quad
2^{x^x}
\end{equation}
\begin{equation}
\nabla^2 f(x,y)=
\frac{\partial^2 f}{\partial x^2}+
\frac{\partial^2 f}{\partial y^2}
\end{equation}
\begin{equation}
\lim_{x\rightarrow 0}
(1+x)^{\frac{1}{x}}=e
\end{equation}
\begin{equation}
\lim_{x\rightarrow 0 }+x^x=1
\end{equation}
\begin{equation}
\sqrt{2}\quad
\sqrt{\frac{x+y}{x-y}}
\end{equation}
\begin{equation}
\sqrt[3]{10}\quad \sqrt[x]{e}
\end{equation}
\begin{equation}
\parallel x\parallel=\sqrt{x} \cdot x
\end{equation}
\begin{equation}
c=1+\sqrt{a}^5+{b}^2
\end{equation}
\begin{equation}
\sqrt[5]{x_1+2x_2-5x_3}
\end{equation}
\begin{equation}
x^{\frac{\pi}{\omega+\theta}}
\end{equation}
\begin{equation}
\lim_{x \to \infty}
\frac{\tan x}{\alpha} = 7
\end{equation}
\begin{equation}
\tan (2\theta) =
\frac{ 2\tan\theta}{ 1-\tan^2\theta.}
\end{equation}
\end{document}
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