Circle of Curvature of ln x

Problem

Curve CF‚™log x with two points A(a, log a), B(b, log b).
P is intersection between normals at A and B respectively.

  1. When b is very near to a, P will limit to a point Q.
    Express the coordinates of Q with a.
  2. With regard to the Q solved in (1), l is the length of segment AQ.
    Express l with a.
  3. Find the value of a when the l is minimum.

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Start with prob.1 !iClick thisj