limit as x approaches 0 of (1+6x)^{1/x}

解答

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

e^{6}

十进制

403.42879 \dots

求解步骤

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

使用指数运算法则

= x \to 0 lim (e^{\frac{1}{x} l n (1 + 6 x)})

使用极限链式法则:

e^{6}

= e^{6}

x \to 0 lim (\frac{2 x ^{2} + x}{5 x})

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x \to 0 lim (\frac{sin ( ω ) x}{x})

x \to 0 lim (- 1 + x)