Limit of \( \displaystyle \frac{\ln{\left(x + 1 \right)}}{x} \) as \( x \to 0 \)

Problem 1.453 · easy

1. \[ \lim_{x \to 0^+}\left(\frac{\ln{\left(x + 1 \right)}}{x}\right) \]
   limitIdentify the limit to be evaluated.✓ Proved
2. \[ = \lim_{x \to 0^+}\left(\frac{\frac{d}{d x} \ln{\left(x + 1 \right)}}{\frac{d}{d x} x}\right) \]
   lhopitalApply L'Hopital's rule because the limit is an indeterminate form 0/0.✓ Proved
3. \[ = \lim_{x \to 0^+} \frac{1}{x + 1} \]
   simplify simplifyCompute the derivatives of the numerator and denominator. Simplify the resulting expression.✓ Proved
4. \[ = 1 \]
   limitEvaluate the limit.✓ Proved