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Beliebt Rechnen >

limit as x approaches 27 of (3-\sqrt[3]{x})/(27-x)

Lösung

x \to 27 lim (\frac{3 - 3 x}{27 - x})

Lösung

\frac{1}{27}

+1

Dezimale

0.03703 \dots

Schritte zur Lösung

x \to 27 lim (\frac{3 - 3 x}{27 - x})

Wende das L'Hopital Theorem an

= x \to 27 lim (\frac{- \frac{1}{3 x ^{\frac{2}{3}}}}{- 1})

Setze den Wert

x = 27

ein

= \frac{- \frac{1}{3 \cdot 2 7 ^{\frac{2}{3}}}}{- 1}

Vereinfache

\frac{- \frac{1}{3 \cdot 2 7 ^{\frac{2}{3}}}}{- 1} : \frac{1}{27}

= \frac{1}{27}

Graph

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