What is the limit as x approaches 0-of (ln(x+1))/x ?

The limit as x approaches 0-of (ln(x+1))/x is 1

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limit as x approaches 0-of (ln(x+1))/x

x \to 0 - lim (\frac{ln ( x + 1 )}{x})

1

Solution steps

x \to 0 - lim (\frac{ln ( x + 1 )}{x})

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

= x \to 0 - lim (ln (x + 1) \frac{1}{x})

Simplify

ln (x + 1) \frac{1}{x} : \frac{ln ( x + 1 )}{x}

= x \to 0 - lim (\frac{ln ( x + 1 )}{x})

Apply L'Hopital's Rule

= x \to 0 - lim (\frac{\frac{1}{x + 1}}{1})

Plug in the value

x = 0

= \frac{\frac{1}{0 + 1}}{1}

Simplify

= 1

What is the limit as x approaches 0-of (ln(x+1))/x ?
The limit as x approaches 0-of (ln(x+1))/x is 1