What is the limit as x approaches 0 of (ln(1-5x))/x ?

The limit as x approaches 0 of (ln(1-5x))/x is -5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

limit as x approaches 0 of (ln(1-5x))/x

x \to 0 lim (\frac{ln ( 1 - 5 x )}{x})

- 5

Solution steps

x \to 0 lim (\frac{ln ( 1 - 5 x )}{x})

Apply L'Hopital's Rule

: x \to 0 lim (\frac{- \frac{5}{1 - 5 x}}{1})

= x \to 0 lim (\frac{- \frac{5}{1 - 5 x}}{1})

Plug in the value

x = 0

= \frac{- \frac{5}{1 - 5 \cdot 0}}{1}

Simplify

\frac{- \frac{5}{1 - 5 \cdot 0}}{1} : - 5

= - 5

x \to \infty lim (a x + b)

x \to 2 - lim (- \frac{3}{x - 2})

x \to \frac{π}{3} - lim (1 - cos (3 x))

x \to - 2 lim (3 x + 2)

x \to 2 - lim (\frac{1}{2 - x})

What is the limit as x approaches 0 of (ln(1-5x))/x ?
The limit as x approaches 0 of (ln(1-5x))/x is -5