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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 1

= \frac{\frac{1}{1}}{1}

Simplify

= 1

x \to 0 + lim (\frac{cos ^{2} ( x )}{x})

x \to - 2 lim ({- 4})

x \to \frac{1}{3} lim ((2 x) (3 x - 3))

x \to - 1 lim (x^{2} + 2 x)

z \to 0 lim (\frac{sin ( 3 z )}{z})

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