(Solved): a) The set of values below contain an error. Consider the difference table for the values up to an ...

a) The set of values below contain an error. Consider the difference table for the values up to and including second differences [See Table 1, Page 5]. Find the error. \&, in the set of values and correct the error, stating all assumptions and showing all calculations. Expand the table to determine \( f(1) \) and \( f(9) \). (12 marks) b) Form a difference table for the set of values below up to and including second difference [See Table 2, Page 6]. By using linear interpolation estimate the value of \( y(6) \) using i. the Newton-Gregory interpolation formula: \( y_{r}=y_{0}+r \Delta y_{0} \), ii. a sketch using similar triangles, and ii. linear Lagrange interpolation.