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

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

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

x \to 1 lim (\frac{1 - \frac{2 l n ( 1 + x )}{x}}{x})

1 - 2 ln (2)

Decimal

- 0.38629 \dots

Solution steps

x \to 1 lim (\frac{1 - \frac{2 l n ( 1 + x )}{x}}{x})

Plug in the value

x = 1

= \frac{1 - \frac{2 l n ( 1 + 1 )}{1}}{1}

Simplify

= 1 - 2 ln (2)

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