These questions are intended to be more challenging than those in Q(1)-(5). (a) The uniform error is defined |x x| 1 + |X| Show that this error converges to both the relative and absolute error in the appropriate limits, and state those limits. (b) Consider the ODE below F = dx dt show that the implicit Euler recurrence relation can be written Xn+1 =axn + b giving expressions for a and b. = 1 + tx [4 marks]