(a) Sketch, on a single diagram, the graphs of \(y=3e^{-2x}\) and \(y=\sec x\) for values of \(x\) such that \(0\le x<\frac\pi2\). [2]

(b) Show that the \(x\)-coordinate of the point of intersection of the two graphs satisfies the equation \(x=\frac12\ln(3\cos x)\). [2]

(c) Use an iterative formula, based on the equation in part (b), to find the \(x\)-coordinate of the point of intersection correct to 3 decimal places. Give the result of each iteration to 5 decimal places. [3]