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\title{Etude de Fonctions}
\author{Aubin SIONVILLE}
\date{MPI Clemenceau - 2021-2023}
\maketitle

\centering

\section*{Equivalence}
\[\boxed{f \sim g \iff \exists u, \begin{cases} f = g \times u \\ u(x) \underset{x \rightarrow u}{\longrightarrow} 1 \end{cases}}\]


\section*{Asymptotes et branches paraboliques}

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        \node {Calcul de $\lim f(x)$}
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                    child[->] {node {$a \in \mathbb{R}$ : Asymptote oblique $y=lx+a$}}
                    child[->] {node {$\pm \infty$ : Branche paraboliques $y=lx$}}
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                child[->] {node {$\pm \infty$ : Branche parabolique de direction asymptotique $Oy$}}
                child[->] {node {$0$ : Branche parabolique de direction asymptotique $Ox$}}
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