(i)[2]
Show that the $x$-coordinate of $P$ obeys $x = \tfrac{1}{2}\ln(40x + 10)$.
(ii)[3]
Apply the iterative relation $x_{n+1} = \tfrac{1}{2}\ln(40x_n + 10)$ with $x_1 = 2.3$ to determine the $x$-coordinate of $P$ correct to $4$ significant figures. Show each iteration to $6$ significant figures.
(iii)[4]
Determine the gradient of the curve at $P$, with the answer correct to $3$ significant figures.
(c(iii))[4]
Determine the gradient of the curve at $P$, with the answer correct to $3$ significant figures.