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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 1

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