NUMERICAL METHODS

Question 1[15 marks] (a) (i) State the fixed point theorem [2 marks] (ii) Verify that the equation f(t) = 13-222-1+2 has roots at 1 =-1, 1 =1 and r = 2. [3 marks) (ii) Show that this equation can be re-writen in the form 1 =9() where 9(1) 1 2 (iv) Determine the converged root if 10 = 1.5. 15 marks] (b) If f(x) = 23 - +1 and 19 = 1, what are 11 and 12 in the Newton iteration. [ 5 marks