limit as x approaches infinity of (1+8/x)^{x/9}

Lösung

x \to \infty lim ((1 + \frac{8}{x})^{\frac{x}{9}})

e^{\frac{8}{9}}

Dezimale

2.43242 \dots

Schritte zur Lösung

x \to \infty lim ((1 + \frac{8}{x})^{\frac{x}{9}})

Wende Exponentenregel an

= x \to \infty lim (e^{\frac{x}{9} l n (1 + \frac{8}{x})})

Wende die Kettenregel für Grenzen an:

e^{\frac{8}{9}}

= e^{\frac{8}{9}}

x \to 0 lim (ln (\frac{1}{x}))

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