limit as x approaches 0+of (3x)^{x^2}

Lösung

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

1

Schritte zur Lösung

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

Vereinfache

(3 x)^{x^{2}} : 3^{x^{2}} x^{x^{2}}

= x \to 0 + lim (3^{x^{2}} x^{x^{2}})

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 0 + lim (3^{x^{2}}) \cdot x \to 0 + lim (x^{x^{2}})

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

x \to 0 + lim (x^{x^{2}}) = 1

= 1 \cdot 1

Vereinfache

= 1

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

x \to 3 lim (- 6 x^{6})

x \to \infty lim (0 - x)

x \to \infty lim (0.1)

x \to 0 lim (x^{2} cos (20 π) x)