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

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

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

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

1

Solution steps

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

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

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

Simplify

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

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

Plug in the value

x = 0

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

Simplify

= 1

x \to 1 lim (\frac{I n x}{x ^{2} - 1})

x \to 5 lim (x^{2} - 3 x + 4)

x \to \infty lim (x e^{3 x})

x \to 0 lim (\frac{1 - co x}{x ^{2}})

x \to - 1 lim (8 + 3 x)

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