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

Problem 1.56 · easy

1. \[ \lim_{x \to 1^+}\left(\frac{\ln{\left(x \right)}}{x - 1}\right) \]
   limitIdentify the limit and the indeterminate form 0/0.✓ Proved
2. \[ = \lim_{x \to 1^+}\left(\frac{\frac{d}{d x} \ln{\left(x \right)}}{\frac{d}{d x} \left(x - 1\right)}\right) \]
   lhopitalApply L'Hôpital's Rule since the limit is of the form 0/0.✓ Proved
3. \[ = \lim_{x \to 1^+} \frac{1}{x} \]
   simplify simplifyCompute the derivatives of the numerator and denominator. Simplify the resulting quotient.✓ Proved
4. \[ = 1 \]
   limitEvaluate the limit as x approaches 1.✓ Proved