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

Lösung

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

\frac{1}{e ^{2}}

Dezimale

0.13533 \dots

Schritte zur Lösung

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

Wende Exponentenregel an

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

Wende die Kettenregel für Grenzen an:

\frac{1}{e ^{2}}

= \frac{1}{e ^{2}}

x \to \frac{π}{2} lim (3 tan (x))

x \to \infty lim (0.6 5^{x})

h (x) \to 0 lim (\frac{f ( x ) ( x + 2 h ( x ) ) - f ( x )}{h ( x )})

x \to - 3 lim (I n x^{2})

x \to 2 lim (\frac{x + 19}{3})