Find the limit of a natural logarithms product function

Asked Jun 18 '20 at 11:16

Active Jun 18 '20 at 11:21

Viewed 35 times

How to find this limit:

$$\lim_{x\to\ 1}\ln x \ln (1-x)$$

I wanted to try L'Hôpital's rule, but it doesn't work here, cause i get:

$$\lim_{x\to\ 1} - \frac{\ln (x)}{1-x} + \frac{\ln (1-x)}{x}$$

asked Jun 18 '20 at 11:16

manabou11

Another one: https://math.stackexchange.com/q/2191534 – Martin R Jun 18 '20 at 11:20
This is not well defined. You probably mean $\lim_{x\to\ 1^-}\ln x \ln (1-x)$. – mwt Jun 18 '20 at 11:23
Also: https://math.stackexchange.com/q/293025. – Martin R Jun 18 '20 at 11:25

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