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

Lösung

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

1

Schritte zur Lösung

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

Wende Exponentenregel an:

(a \cdot b)^{n} = a^{n} b^{n}

= n \to 0 + lim (3^{\frac{n}{2}} n^{\frac{n}{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

= n \to 0 + lim (3^{\frac{n}{2}}) \cdot n \to 0 + lim (n^{\frac{n}{2}})

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

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

= 1 \cdot 1

Vereinfache

= 1

x \to - \frac{π}{2} - lim (- 8 x - \frac{π}{2})

x \to 0 lim (x cos (e^{\frac{2}{x}}))

x \to \infty lim (G (x))

x \to 6 lim ((x - 5) (x - 7))

x \to 2 lim (f (x) 3)