6.2 Natürliche Exponentialfunktion

Info

$e$ - Eulerzahl $e = 2, 718 \dots$ (irrationale Zahll

Eigenschaften der Funttion $f (x) = e^{x}$

\begin{aligned} f (0) = 1 \\ lim_{x \to + \infty} e^{x} = + \infty \\ lim_{x \to - \infty} e^{x} = 0 \end{aligned}

- lim_{x \to + \infty} e^{a x} ? a \in R ∖ {0}

\begin{array}{ll} Fallunterscheidung \\ a > 0 lim_{x \to \infty} e^{a x} = + \infty \\ a < 0 lim_{x \to \infty} e^{a x} = 0 \end{array}

\begin{aligned} f (x) & = e^{x} - 2 \\ e^{x} - 2 & = 0 + 2 \\ e^{x} & = 2 & ∣ \ln \\ x & = \ln_{2} \\ x_{0} & = 0, 693 \end{aligned}

$W_{f} : h () x) > 2$
$W_{f} : h (x) \in R^{+} mit h (x) > 2$
$W_{f} : h (x)] 2; \infty]$