What is the limit as x approaches 0 of (ln(1-6x))/x ?

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

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

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

- 6

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

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

= - 6

x \to - 8 lim (\frac{∣ x + 8 ∣}{x + 8})

- \frac{4 x}{y}

f (x) = x cos (x)

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{5}}}}{x ^{6}} d x

x \to 2 - lim (x - a)

What is the limit as x approaches 0 of (ln(1-6x))/x ?
The limit as x approaches 0 of (ln(1-6x))/x is -6