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

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

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

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

- 1

Solution steps

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

Simplify

\frac{1}{1 - x} ln (x) : \frac{ln ( x )}{1 - x}

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

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 - 9 lim ((18 - x)^{\frac{4}{3}})

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

x \to 1 lim (\frac{4}{x ^{2} - 2 x + 1})

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

t \to 0 lim (\frac{t ^{2}}{1 - cos ^{2} ( t )})

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