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

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

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

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

1

Solution steps

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

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

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

Simplify

\frac{1}{x} ln (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

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x \to 2 lim (12)

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