limit as x approaches 0 of (1-x)^{(1/x)}

Lösung

x \to 0 lim ((1 - x)^{(\frac{1}{x})})

\frac{1}{e}

Dezimale

0.36787 \dots

Schritte zur Lösung

x \to 0 lim ((1 - x)^{\frac{1}{x}})

Wende Exponentenregel an

= x \to 0 lim (e^{\frac{1}{x} l n (1 - x)})

Wende die Kettenregel für Grenzen an:

\frac{1}{e}

= \frac{1}{e}

x \to 2 lim (3 x^{3} - 2 x + 7)

x \to 0 lim ([\frac{1}{x}])

x \to - 3 lim (2 x^{3} + 6 x^{2} - 9)

x \to \infty lim (\frac{1}{3 x + 1})

x \to 2 lim (x^{3} - 5 x^{2} + 7 x + 1)