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人気のある微分積分 >

limit as x approaches 0 of ((1+3^x)/2)^{1/x}

解

x \to 0 lim ((\frac{1 + 3 ^{x}}{2})^{\frac{1}{x}})

解

3

+1

十進法表記

1.73205 \dots

解答ステップ

x \to 0 lim ((\frac{1 + 3 ^{x}}{2})^{\frac{1}{x}})

指数の規則を適用する

= x \to 0 lim (e^{\frac{1}{x} l n (\frac{1 + 3 ^{x}}{2})})

連鎖法則の制限を適用する:

3

= 3

グラフ

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