limit as x approaches 125 of (x-125)/(\sqrt[3]{x)-5}

解答

x \to 125 lim (\frac{x - 125}{3 x - 5})

75

求解步骤

x \to 125 lim (\frac{x - 125}{3 x - 5})

使用洛必达法则

= x \to 125 lim (\frac{1}{\frac{1}{3 x ^{\frac{2}{3}}}})

代入值

x = 125

= \frac{1}{\frac{1}{3 \cdot 12 5 ^{\frac{2}{3}}}}

化简

\frac{1}{\frac{1}{3 \cdot 12 5 ^{\frac{2}{3}}}} : 75

= 75

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