4 The equation \(x = \frac { 10 } { \mathrm { e } ^ { 2 x } - 1 }\) has one positive real root, denoted by \(\alpha\).
- Show that \(\alpha\) lies between \(x = 1\) and \(x = 2\).
- Show that if a sequence of positive values given by the iterative formula
$$x _ { n + 1 } = \frac { 1 } { 2 } \ln \left( 1 + \frac { 10 } { x _ { n } } \right)$$
converges, then it converges to \(\alpha\).
- Use this iterative formula to determine \(\alpha\) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.