What is the limit as x approaches 0 of (ln(1-3x))/x ?

The limit as x approaches 0 of (ln(1-3x))/x is -3

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limit as x approaches 0 of (ln(1-3x))/x

x \to 0 lim (\frac{ln ( 1 - 3 x )}{x})

- 3

Solution steps

x \to 0 lim (\frac{ln ( 1 - 3 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- \frac{3}{1 - 3 x}}{1})

= x \to 0 lim (\frac{- \frac{3}{1 - 3 x}}{1})

Plug in the value

x = 0

= \frac{- \frac{3}{1 - 3 \cdot 0}}{1}

Simplify

\frac{- \frac{3}{1 - 3 \cdot 0}}{1} : - 3

= - 3

\int 15 x^{2} - cos (x) + C x + C d x

f (x) = \frac{( x ^{2} - 4 x )}{x + 1}

x \to 0 + lim (ln (\frac{7}{x ^{5}}))

15 y^{^{''}} + 7 y^{^{'}} - 2 y = 0

\int sin (π x) cos (π x) d x

What is the limit as x approaches 0 of (ln(1-3x))/x ?
The limit as x approaches 0 of (ln(1-3x))/x is -3