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

\int \frac{x ^{3}}{1 + x ^{2} - x ^{4}} d x

\frac{d}{d x} (x^{3} sin (\frac{1}{x}))

\frac{d}{d y} (\frac{x y}{x ^{2} + y ^{2}})

f (x) = \frac{2 - 5 x}{e ^{x}}

x \to \infty lim (5^{x})

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