What is the limit as x approaches 0-of (ln(1-x))/x ?

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

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

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

- 1

Solution steps

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})

Simplify

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= - 1

x \to 0 lim (\frac{2}{3 x})

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

x \to \frac{3}{4} lim (x)

x \to 1 lim (x + 5)

θ \to \frac{π}{2 ^{+}} lim (sec (θ))

What is the limit as x approaches 0-of (ln(1-x))/x ?
The limit as x approaches 0-of (ln(1-x))/x is -1