(a(i))[2]
Show by drawing a suitable pair of graphs that the equation $e^{2x} = 2 - x$ has only one root.
(a(ii))[2]
Verify by calculation that this root lies between $x = 0$ and $x = 0.5$.
(a(iii))[1]
Show that, if a sequence of values produced by the iterative formula $x_{n+1} = \tfrac{1}{2}\ln(2 - x_n)$ converges, then its limit is the root of the equation in part (i).
(a(iv))[3]
Use this iterative formula, with initial value $x_1 = 0.25$, to find the root correct to $2$ decimal places. State the value from each iteration to $4$ decimal places.