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人気のある微分積分 >

limit as x approaches 0 of (\sqrt[3]{x+1}+x-1)/x

解

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

解

\frac{4}{3}

+1

十進法表記

1.33333 \dots

解答ステップ

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

ロピタルの定理を適用する

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

値を挿入する

x = 0

= \frac{\frac{1}{3 ( 0 + 1 ) ^{\frac{2}{3}}} + 1}{1}

簡素化

\frac{\frac{1}{3 ( 0 + 1 ) ^{\frac{2}{3}}} + 1}{1} : \frac{4}{3}

= \frac{4}{3}

グラフ

人気の例

limit as x approaches 0 of sin((3x)/x)

x \to 0 lim (sin (\frac{3 x}{x}))

limit as x approaches 0 of (1+x/4)^{1/x}

x \to 0 lim ((1 + \frac{x}{4})^{\frac{1}{x}})

limit as x approaches-1 of x^3-3x+2

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

limit as x approaches 2 of (x-1)/(x+1)

x \to 2 lim (\frac{x - 1}{x + 1})

limit as x approaches 0 of 1/(arcsin(x))

x \to 0 lim (\frac{1}{arcsin ( x )})