limit as x approaches 0 of (e^x-1)/(6x)

解

x \to 0 lim (\frac{e ^{x} - 1}{6 x})

\frac{1}{6}

十進法表記

0.16666 \dots

解答ステップ

x \to 0 lim (\frac{e ^{x} - 1}{6 x})

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

= \frac{1}{6} \cdot x \to 0 lim (\frac{e ^{x} - 1}{x})

ロピタルの定理を適用する

= \frac{1}{6} \cdot x \to 0 lim (\frac{e ^{x}}{1})

値を挿入する

x = 0

= \frac{1}{6} \cdot \frac{e ^{0}}{1}

簡素化

\frac{1}{6} \cdot \frac{e ^{0}}{1} : \frac{1}{6}

= \frac{1}{6}