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Beliebt Rechnen >

limit as x approaches 0 of 1/x ln(1-6x)

Lösung

x \to 0 lim (\frac{1}{x} ln (1 - 6 x))

Lösung

- 6

Schritte zur Lösung

x \to 0 lim (\frac{1}{x} ln (1 - 6 x))

Vereinfache

\frac{1}{x} ln (1 - 6 x) : \frac{ln ( 1 - 6 x )}{x}

= x \to 0 lim (\frac{ln ( 1 - 6 x )}{x})

Wende das L'Hopital Theorem an

= x \to 0 lim (\frac{- \frac{6}{1 - 6 x}}{1})

Setze den Wert

x = 0

ein

= \frac{- \frac{6}{1 - 6 \cdot 0}}{1}

Vereinfache

\frac{- \frac{6}{1 - 6 \cdot 0}}{1} : - 6

= - 6

Graph

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