What is the limit as x approaches 0+of (ln(1+3x))/x ?

The limit as x approaches 0+of (ln(1+3x))/x is 3

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limit as x approaches 0+of (ln(1+3x))/x

x \to 0 + lim (\frac{ln ( 1 + 3 x )}{x})

3

Solution steps

x \to 0 + lim (\frac{ln ( 1 + 3 x )}{x})

Apply L'Hopital's Rule

: x \to 0 + lim (\frac{\frac{3}{1 + 3 x}}{1})

= x \to 0 + lim (\frac{\frac{3}{1 + 3 x}}{1})

Plug in the value

x = 0

= \frac{\frac{3}{1 + 3 \cdot 0}}{1}

Simplify

= 3

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x \to - 3 lim (- x^{3} - 3 x)

x \to \infty lim (- 4 \cdot x)

What is the limit as x approaches 0+of (ln(1+3x))/x ?
The limit as x approaches 0+of (ln(1+3x))/x is 3