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\begin{document}
  
  \title{template_assignment} % Article title
  \fancyhead[C]{}
  \begin{minipage}{0.295\textwidth} % Left title
    \raggedright
    Julian Steinmann 
    \medskip\hrule
  \end{minipage}
  \begin{minipage}{0.4\textwidth} % Center title
    \centering 
    \large
    Beispiel \(\mathcal{O}\)-Notation \\ % Assignment 
    \normalsize
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  \begin{minipage}{0.295\textwidth} % Right title 
    \raggedleft
    \today 
    \medskip\hrule
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  \section*{}

  Sei folgende Aufgabe gegeben: \\
  \subsection{}
  Zeigen oder widerlegen Sie \(\log(n^n) \le \mathcal{O}(4n)\).
  
  \begin{align*}
      \lim_{n\to \infty} \frac{\log(n^n)}{4n} &= \lim_{n\to \infty} \frac{n \log n}{4n} \\ &= \lim_{n\to\infty} \frac{\log n + 1}{4} \quad \text{ (L'Hopital)}\\ &= \infty
  \end{align*}
  also gilt mit Theorem 1.1 aus dem Skript \(\log(n^n) \nleq \mathcal{O}(4n)\).
  \bigskip
\end{document}