limit as x approaches 0+of (x/(34))^x

解

x \to 0 + lim ((\frac{x}{34})^{x})

1

解答ステップ

x \to 0 + lim ((\frac{x}{34})^{x})

指数の規則を適用する

= x \to 0 + lim (\frac{x ^{x}}{3 4 ^{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 +} ( x ^{x} )}{lim _{x \to 0 +} ( 3 4 ^{x} )}

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

x \to 0 + lim (3 4^{x}) = 1

= \frac{1}{1}

簡素化

= 1