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

Lösung

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

e^{2}

Dezimale

7.38905 \dots

Schritte zur Lösung

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

Vereinfache

(\frac{x + 1}{x - 1})^{x - 1} : (\frac{x + 1}{x - 1})^{x} (\frac{x + 1}{x - 1})^{- 1}

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

x \to a lim [f (x) \cdot g (x)] = x \to a lim f (x) \cdot x \to a lim g (x)

mit Einschränkung des unbestimmten Ausdrucks

= x \to \infty lim ((\frac{x + 1}{x - 1})^{x}) \cdot x \to \infty lim ((\frac{x + 1}{x - 1})^{- 1})

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

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

= e^{2} \cdot 1

Vereinfache

= e^{2}

x \to 0 lim (\frac{1 + x ^{2} - 3 1 - 2 x}{x})

x \to 0 + lim (7 x ln (x))

x \to 0 + lim (e^{- \frac{1}{x}} \cdot x^{- 2})

x \to 0 lim (x^{2} sin (\frac{π}{x}))

x \to 3 lim (x - 7)