What is the limit as n approaches 0+of (3(n))^{n/2} ?

The limit as n approaches 0+of (3(n))^{n/2} is 1

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

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

1

Solution steps

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

Apply exponent rule:

(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)

With the exception of indeterminate form

= 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

Simplify

= 1

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

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

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

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

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

What is the limit as n approaches 0+of (3(n))^{n/2} ?
The limit as n approaches 0+of (3(n))^{n/2} is 1