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

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

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

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

1

Solution steps

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

Simplify

\frac{1}{x} ln (x + 1) : \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 1/x*ln(x+1) ?
The limit as x approaches 0 of 1/x*ln(x+1) is 1