limit as x approaches 0 of (e^x-1)/(7x)

解答

x \to 0 lim (\frac{e ^{x} - 1}{7 x})

\frac{1}{7}

十进制

0.14285 \dots

求解步骤

x \to 0 lim (\frac{e ^{x} - 1}{7 x})

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

= \frac{1}{7} \cdot x \to 0 lim (\frac{e ^{x} - 1}{x})

使用洛必达法则

= \frac{1}{7} \cdot x \to 0 lim (\frac{e ^{x}}{1})

代入值

x = 0

= \frac{1}{7} \cdot \frac{e ^{0}}{1}

化简

\frac{1}{7} \cdot \frac{e ^{0}}{1} : \frac{1}{7}

= \frac{1}{7}

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