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人気のある微分積分 >

limit as x approaches infinity of e^{9xln(1+1/(7x))}

解

x \to \infty lim (e^{9 x l n (1 + \frac{1}{7 x})})

解

e^{\frac{9}{7}}

+1

十進法表記

3.61725 \dots

解答ステップ

x \to \infty lim (e^{9 x l n (1 + \frac{1}{7 x})})

簡素化

e^{9 x l n (1 + \frac{1}{7 x})} : (1 + \frac{1}{7 x})^{9 x}

= x \to \infty lim ((1 + \frac{1}{7 x})^{9 x})

指数の規則を適用する

= x \to \infty lim (e^{9 x l n (1 + \frac{1}{7 x})})

連鎖法則の制限を適用する:

e^{\frac{9}{7}}

= e^{\frac{9}{7}}

グラフ

人気の例

limit as x approaches 0 of sin(|x|)

x \to 0 lim (sin (∣ x ∣))

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

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