What is the limit as x approaches 3 of (ln(x+1))/x ?

The limit as x approaches 3 of (ln(x+1))/x is 2/3 ln(2)

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limit as x approaches 3 of (ln(x+1))/x

x \to 3 lim (\frac{ln ( x + 1 )}{x})

\frac{2}{3} ln (2)

Decimal Notation

0.46209 \dots

Solution steps

x \to 3 lim (\frac{ln ( x + 1 )}{x})

Plug in the value

x = 3

= \frac{ln ( 3 + 1 )}{3}

Simplify

\frac{ln ( 3 + 1 )}{3} : \frac{2}{3} ln (2)

= \frac{2}{3} ln (2)

x \to 3 lim (\frac{1}{x + 1})

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

x \to 3 lim (\frac{cos ( 1 )}{x})

x \to 3 lim (\frac{( x + 1 )}{x})

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

What is the limit as x approaches 3 of (ln(x+1))/x ?
The limit as x approaches 3 of (ln(x+1))/x is 2/3 ln(2)