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

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

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

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

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

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

Plug in the value

x = 1

= \frac{ln ( 1 + 1 )}{1}

Simplify

= ln (2)

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