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

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

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

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

1

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

x = 0

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

Simplify

= 1

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