(a)[2]
On one diagram, sketch the graphs of $y = 3e^{-2x}$ and $y = \sec x$ for values of $x$ such that $0 \leq x < \frac{1}{2}\pi$.
(b)[2]
Show that the $x$-coordinate of the point where the two graphs meet satisfies the equation $x = \frac{1}{2} \ln(3\cos x)$.
(c)[3]
Use the iterative formula, based on the equation in part (b), to determine the $x$-coordinate of the point of intersection correct to 3 decimal places. Show the result from each iteration to 5 decimal places.