Somme de limites
$$ \begin{array}{|c|c|c|c|} \hline \begin{array}{ll} & \hspace{-1em}\lim f (x) \\ \lim g (x) & \end{array} & \mathcal{l} & +\infty & -\infty \\ \hline \mathcal{l}' & \mathcal{l} + \mathcal{l}' & +\infty & -\infty \\ \hline +\infty & +\infty & +\infty & ? \\ \hline -\infty & -\infty & ? & -\infty \\ \hline \end{array} $$
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Produit de limites
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\( \begin{array}{ll} & \hspace{-1em}\lim f (x) \\ \lim g (x) & \end{array} \)
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\( \mathcal{l} \gt 0 \)
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\( \mathcal{l} \lt 0 \)
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\( \mathcal{l} = 0 \)
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\( +\infty \)
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\( -\infty \)
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\( \mathcal{l}' \gt 0 \)
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\( \mathcal{l} \times \mathcal{l}' \)
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\( +\infty \)
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\( -\infty \)
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\( \mathcal{l}' \lt 0 \)
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\( -\infty \)
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\( +\infty \)
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\( \mathcal{l}'=0 \)
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\( ? \)
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\( ? \)
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\( +\infty \)
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\( +\infty \)
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\( -\infty \)
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\( ? \)
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\( +\infty \)
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\( -\infty \)
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\( -\infty \)
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\( -\infty \)
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\( +\infty \)
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\( ? \)
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\( -\infty \)
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\( +\infty \)
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Quotient de limites
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\( \begin{array}{ll} & \hspace{-1em}\lim f (x) \\ \lim g (x) & \end{array} \)
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\( \mathcal{l} \gt 0 \)
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\( \mathcal{l} \lt 0 \)
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\( \mathcal{l} = 0 \)
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\( +\infty \)
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\( -\infty \)
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\( \mathcal{l}' \gt 0 \)
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\( \frac{\mathcal{l}}{\mathcal{l}'} \)
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\( +\infty \)
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\( +\infty \)
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\( -\infty \)
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\( \mathcal{l}' \lt 0 \)
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\( -\infty \)
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\( -\infty \)
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\( +\infty \)
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\( \mathcal{l}'=0^+ \)
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\( +\infty \)
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\( -\infty \)
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\( 0 \)
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\( +\infty \)
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\( -\infty \)
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\( \mathcal{l}'=0^- \)
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\( -\infty \)
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\( +\infty \)
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\( -\infty \)
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\( +\infty \)
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\( +\infty \)
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\( 0^+ \)
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\( 0^- \)
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\( 0 \)
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\( ? \)
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\( -\infty \)
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\( 0^- \)
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\( 0^+ \)
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\( 0 \)
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