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

Lösung

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

75

Schritte zur Lösung

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

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 125

ein

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

Vereinfache

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

= 75

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