limit as x approaches 0+of x^{x^x}-1

Lösung

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

- 1

Schritte zur Lösung

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

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

mit Einschränkung des unbestimmten Ausdrucks

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

x \to 0 + lim (x^{x^{x}}) = 0

x \to 0 + lim (1) = 1

= 0 - 1

Vereinfache

= - 1

x \to \frac{π}{2} lim ((2 x - π) tan (x))

x \to 1 + lim (tan (x - 1))

x \to 4 lim (\frac{2 x - 4}{x - 1})

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

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