limit as x approaches 0-of 2/(1-2^{1/x)}

解

x \to 0 - lim (\frac{2}{1 - 2 ^{\frac{1}{x}}})

2

解答ステップ

x \to 0 - lim (\frac{2}{1 - 2 ^{\frac{1}{x}}})

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

= 2 \cdot x \to 0 - lim (\frac{1}{1 - 2 ^{\frac{1}{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

= 2 \cdot \frac{lim _{x \to 0 -} ( 1 )}{lim _{x \to 0 -} ( 1 - 2 ^{\frac{1}{x}} )}

x \to 0 - lim (1) = 1

x \to 0 - lim (1 - 2^{\frac{1}{x}}) = 1

= 2 \cdot \frac{1}{1}

簡素化

= 2