Consider the following tabular data: \(\ln 9.0=2.1972, \ln 9.5=2.2513\), and \(\ln 11.0=2.3979\).

(a) Calculate the Lagrange interpolation polynomial \(p_{2}(x)\) and compute approximations of \(\ln 9.4, \ln 10, \ln 10.5, \ln 11.5, \ln 12\). Evaluate the errors by using exact values to four decimal places.

(b) Comment on the effect of extrapolation.

(c) Set up Newton's divided difference formula for the same data, and derive from it \(p_{2}(x)\).