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})

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

= - 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

= - 6

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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