- (a) On the same diagram, sketch and clearly label the graphs with equations
$$y = \mathrm { e } ^ { x } \quad \text { and } \quad y = 10 - x$$
Show on your sketch the coordinates of each point at which the graphs cut the axes.
(b) Explain why the equation \(\mathrm { e } ^ { x } - 10 + x = 0\) has only one solution.
(c) Show that the solution of the equation
$$\mathrm { e } ^ { x } - 10 + x = 0$$
lies between \(x = 2\) and \(x = 3\)
(d) Use the iterative formula
$$x _ { n + 1 } = \ln \left( 10 - x _ { n } \right) , \quad x _ { 1 } = 2$$
to calculate the values of \(x _ { 2 } , x _ { 3 }\) and \(x _ { 4 }\).
Give your answers to 4 decimal places.