(i)[3]
Find the gradient at point $P$ on the curve.
(ii)[2]
Show that the $x$-coordinate of point $M$ satisfies the equation $x = \frac{x + 0.5}{\ln x}$.
(iii)[3]
Use an iterative formula based on the equation in part (ii) to determine the $x$-coordinate of $M$, correct to $4$ significant figures. Record each iteration to $6$ significant figures.
(c(ii))[2]
Show that the $x$-coordinate of point $M$ satisfies the equation $x = \frac{x + 0.5}{\ln x}$.
(c(iii))[3]
Use the iteration from part (ii) to determine the $x$-coordinate of $M$, correct to $4$ significant figures. Display each iteration to $6$ significant figures.