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

The limit as x approaches 1 of (ln(x+1))/x is ln(2)

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

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

ln (2)

Decimal

0.69314 \dots

Solution steps

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

Plug in the value

x = 1

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

Simplify

= ln (2)

x \to 3 - lim (ln (3 - x))

t \to \frac{1}{3} lim (5 t - 7)

x \to \infty lim ((1 + sin (\frac{3}{x}))^{x + 1})

x \to 0 lim (\frac{x}{x ^{3}})

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

What is the limit as x approaches 1 of (ln(x+1))/x ?
The limit as x approaches 1 of (ln(x+1))/x is ln(2)