What is the limit as x approaches 1 of (1-x^2)/(ln(x)) ?

The limit as x approaches 1 of (1-x^2)/(ln(x)) is -2

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limit as x approaches 1 of (1-x^2)/(ln(x))

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

- 2

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 1

= \frac{- 2 \cdot 1}{\frac{1}{1}}

Simplify

= - 2

What is the limit as x approaches 1 of (1-x^2)/(ln(x)) ?
The limit as x approaches 1 of (1-x^2)/(ln(x)) is -2