limit as x approaches 0+of (1/x)^{3x}

解

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

1

解答ステップ

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

指数の規則を適用する

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

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

x \to 0 + lim (1) = 1

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

= \frac{1}{1}

簡素化

= 1