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

Lösung

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

1

Schritte zur Lösung

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

\frac{ln ( 1 - x )}{x} = ln (1 - x) \frac{1}{x}

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

Vereinfache

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

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

Wende das L'Hopital Theorem an

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

Setze den Wert

x = 0

ein

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

Vereinfache

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

= 1

x \to - 3 lim (\frac{- x}{3 x + 9})

x \to 3 lim (\frac{[ x ] - 3}{x - 3})

x \to c lim (a x^{2} + b)

x \to 0 lim ((\frac{1}{x})^{2})

x \to 0 lim (x ln (2 x))