limit as x approaches infinity of (1-1/(4x))^{8x}

解答

x \to \infty lim ((1 - \frac{1}{4 x})^{8 x})

\frac{1}{e ^{2}}

十进制

0.13533 \dots

求解步骤

x \to \infty lim ((1 - \frac{1}{4 x})^{8 x})

使用指数运算法则

= x \to \infty lim (e^{8 x l n (1 - \frac{1}{4 x})})

使用极限链式法则:

\frac{1}{e ^{2}}

= \frac{1}{e ^{2}}

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