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})

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})

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

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

= 1

x \to 1 + lim (ln (x^{x}))

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

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

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

x \to - \infty lim (x - 3)

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