(i)[3]
By sketching an appropriate pair of graphs, demonstrate that the equation $3\ln x = 15 - x^3$ has exactly one real root.
(ii)[2]
Use calculation to show that the root is between $2.0$ and $2.5$.
(iii)[3]
Apply the iterative formula $x_{n+1} = \sqrt[3]{(15 - 3\ln x_n)}$ to determine the root correct to 3 decimal places. Record each iteration to 5 decimal places.