limit as x approaches infinity of (1-3/x)^{x^2}

Lösung

x \to \infty lim ((1 - \frac{3}{x})^{x^{2}})

0

Schritte zur Lösung

x \to \infty lim ((1 - \frac{3}{x})^{x^{2}})

Wende Exponentenregel an

= x \to \infty lim (e^{x^{2} l n (1 - \frac{3}{x})})

Wende die Kettenregel für Grenzen an:

0

= 0

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

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

x \to 1 lim (x^{2} - 5 x + 6)

x \to \infty - lim (x)

x \to 3 lim (\frac{x ^{4} - 3}{x - 3})