Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram displays sections of the curves given by $y = 4e^{-2x}$ and $y = 1 + 0.5\sin 3x$. $P$ marks one point where the curves intersect, and the shaded part is enclosed by the two curves together with the $y$-axis.
(a)[1]
Show that the $x$-coordinate of $P$ obeys the equation $x = -0.5\ln(0.25 + 0.125\sin 3x)$.
(b)[3]
Use an iterative method, based on the equation in part (a), to determine the $x$-coordinate of $P$ correct to 4 significant figures. Begin with $0.5$ and record each iteration to 6 significant figures.
(c)[4]
Hence determine the area of the shaded region. Provide 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 $4e^{-2x}=1+0.5\sin 3x$ and verify $x=-0.5\ln(0.25+0.125\sin 3x)$” …