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 - 6 + lim (x + 6 + x)

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

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

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

x \to 0 lim (\frac{5 x}{3 x})

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