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

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

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

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

1

Solution steps

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

Simplify

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

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

Apply L'Hopital's Rule

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

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

Plug in the value

x = 0

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

Simplify

= 1

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