limit as x approaches infinity of ((x+1)/(x+3))^{x/5}

解答

x \to \infty lim ((\frac{x + 1}{x + 3})^{\frac{x}{5}})

\frac{1}{e ^{\frac{2}{5}}}

十进制

0.67032 \dots

求解步骤

x \to \infty lim ((\frac{x + 1}{x + 3})^{\frac{x}{5}})

使用指数运算法则

= x \to \infty lim (e^{\frac{x}{5} l n (\frac{x + 1}{x + 3})})

使用极限链式法则:

\frac{1}{e ^{\frac{2}{5}}}

= \frac{1}{e ^{\frac{2}{5}}}

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