limit as k approaches infinity of (k^{1/k})/(ln(k))

解

k \to \infty lim (\frac{k ^{\frac{1}{k}}}{ln ( k )})

0

解答ステップ

k \to \infty lim (\frac{k ^{\frac{1}{k}}}{ln ( k )})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

不定形式の場合を除く

= \frac{lim _{k \to \infty} ( k ^{\frac{1}{k}} )}{lim _{k \to \infty} ( ln ( k ) )}

k \to \infty lim (k^{\frac{1}{k}}) = 1

k \to \infty lim (ln (k)) = \infty

= \frac{1}{\infty}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0