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Beliebt Rechnen >

limit as x approaches 8 of (sqrt(7+\sqrt[3]{x)}-3)/(x-8)

Lösung

x \to 8 lim (\frac{7 + 3 x - 3}{x - 8})

Lösung

\frac{1}{72}

+1

Dezimale

0.01388 \dots

Schritte zur Lösung

x \to 8 lim (\frac{7 + 3 x - 3}{x - 8})

Wende das L'Hopital Theorem an

= x \to 8 lim \frac{\frac{1}{6 x ^{\frac{2}{3}} 3 x + 7}}{1}

Setze den Wert

x = 8

ein

= \frac{\frac{1}{6 \cdot 8 ^{\frac{2}{3}} 3 8 + 7}}{1}

Vereinfache

\frac{\frac{1}{6 \cdot 8 ^{\frac{2}{3}} 3 8 + 7}}{1} : \frac{1}{72}

= \frac{1}{72}

Graph

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