3. The root of the equation \(\mathrm { f } ( x ) = 0\), where
$$f ( x ) = x + \ln 2 x - 4$$
is to be estimated using the iterative formula \(x _ { n + 1 } = 4 - \ln 2 x _ { n }\), with \(x _ { 0 } = 2.4\).
- Showing your values of \(x _ { 1 } , x _ { 2 } , x _ { 3 } , \ldots\), obtain the value, to 3 decimal places, of the root.
- By considering the change of sign of \(\mathrm { f } ( x )\) in a suitable interval, justify the accuracy of your answer to part (a).