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

Lösung

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

e^{3}

Dezimale

20.08553 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Wende die Kettenregel für Grenzen an:

e^{3}

= e^{3}

r \to 0 lim (1 + \frac{1}{r} + \frac{1}{r ^{2}})

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

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

x \to 3 + lim (2 x - 1)

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