Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram displays sections of the curves $y = 4e^{-2x}$ and $y = 1 + 0.5\sin 3x$. Point $P$ is where the curves intersect, and the shaded area is enclosed by the two curves and the $y$-axis.
(a)[1]
Show that the $x$-coordinate of $P$ obeys $x = -0.5\ln(0.25 + 0.125\sin 3x)$.
(b)[3]
Apply an iterative formula based on the equation from part (a) to determine the $x$-coordinate of $P$ correct to 4 significant figures. Start from $0.5$ and write each iterated value to 6 significant figures.
(c)[4]
Hence determine the area of the shaded region. Give your answer correct to 2 significant figures.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State $4e^{-2x}=1+0.5\sin3x$ and verify $x=-0.5\ln(0.25+0.125\sin3x)$” …