(i)[3]
Show that $p$ is a solution of the equation $\ln x = 1 + \frac{3}{x}$.
(ii)[2]
By sketching appropriate graphs, demonstrate that the equation in part (i) has just one root.
(iii)[3]
You are told that the equation in part (i) may be rearranged as $x = \frac{3 + x}{\ln x}$. Use an iterative formula based on this rearrangement to find $p$ correct to $2$ decimal places. Record the result of each iteration to $4$ decimal places.
(c(ii))[2]
By sketching appropriate graphs, demonstrate that the equation in part (i) has only one root.
(c(iii))[3]
You are told that the equation in part (i) may be expressed as $x = \frac{3 + x}{\ln x}$. Use an iterative formula based on this rearrangement to find $p$ correct to 2 decimal places, and give each iteration result to 4 decimal places.