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

解

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

- \infty

解答ステップ

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

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

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

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

不定形式の場合を除く

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

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

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

= 1 \cdot (- \infty)

無限大の特性を適用する:

c \cdot (- \infty) = - \infty

= - \infty