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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 1

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

Simplify

= 1

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