latex-skript/exercises/maths/math-formulas.rend.tex

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\documentclass[a4paper, ngerman]{report}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage{eurosym, tipa, textcomp, textgreek, upgreek}
\usepackage{amssymb, amsfonts, amsmath, dsfont}
\usepackage[hidelinks]{hyperref}
\usepackage{cleveref}
\usepackage{graphicx}
\usepackage{longtable, array, tabularx, booktabs, colortbl}
\usepackage{minted}
\begin{document}
\thispagestyle{empty}
\hrule
\begin{center}
\textbf{Gravitational acceleration in Germany}
$$9,81\,\frac{m}{s^2}$$ \\
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\textbf {\textit{pq} formula}
$$x_{1,2} = - \frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2 - q}$$ \\
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\textbf{Quadratic formula}
$$x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ \\
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\textbf{Catalan numbers}
\begin{equation*} C_n = \frac{1}{n+1} {2n \choose n} = \frac{(2n)!}{(n+1)!n!} \end{equation*} \\
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\textbf{Definition of a factorial}
$$n! = \prod_{i=1}^{n} i$$ \\
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\textbf{Set of all odd natural numbers}
$$\{ x \mid x \in \mathds{N}, \text{odd}(x) \}$$
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\textbf{Elimination $\neg\exists x$}
$$\neg\exists x . p(x) \Leftrightarrow \forall x . \neg p(x)$$
\end{center}
\hrule
\end{document}