3. O B C f(x ) = - -1+In *x 2x The diagram above shows part of the curve with equation y = f(x). The curve crosses the x-axis at the points A and B, and has a minimum at the point C. (a) Show that the x-coordinate of Cis . (5) Ifelement (b) Find the y-coordinate of C in the form & In 2, where k is a constant. (2) (c) Verify that the x-coordinate of B lies between 4.905 and 4.915. (2) (d) Show that the equation 2x - 1 + In ~ =0 can be rearranged into the form x = 2e (-#) (2) The x-coordinate of B is to be found using the iterative formula Xu+1 = 2e 239 with xo = 5. (e) Calculate, to 4 decimal places, the values of x1, x2 and x3. (2) (Total 13 marks) Edexcel Internal Review C3 Numerical Methods - Location of roots f(x) = x' - 2- * *0. (a) Show that the equation f(x) = 0 has a root between 1 and 2. (2) An approximation for this root is found using the iteration formula Xn+ 1 = 2 + 1 ]' with x, = 1.5. (b) By calculating the values of x1, X2, x3 and x4, find an approximation to this root, giving your answer to 3 decimal places. (4) (c) By considering the change of sign of f(x) in a suitable interval, verify that your answer to part (b) is correct to 3 decimal places. pdfelemerit (2) (Total 8 marks)