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\vskip -1cm\fbox{\huge L'exponentielle}

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$exp(x)$ se note aussi $e^x$

$e^0 = 1$\qquad $e^1 = e \approx 2,72$

$e^{-1}\approx 0,37$\qquad $e^x>0$

$e^A\times e^B = e^{A+B}$

$e^{-A} = \dfrac{1}{e^A}$

$\dfrac{e^A}{e^B} = e^{A-B}$


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$\lim\limits_{x\to-\infty} e^x = 0_+$

$\lim\limits_{x\to+\infty} e^x = +\infty$

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$\lim\limits_{x\to+\infty} \dfrac{e^x}{x} = +\infty$

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Pour tout $n\in\N$, $\lim\limits_{x\to-\infty} x^ne^{x} = 0$

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$(e^x)' = e^x$

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$(e^u)' = u'\times e^u$
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Utilisation possible :

\begin{itemize}
  \item Étude de fonctions : dérivées, limites, variations
  \item Croissance et décroissance exponentielles
  \item Finance : intérêts composés
  \item Physique : refroidissement, charge d'un condensateur
  \item Probabilités : loi exponentielle
\end{itemize}

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