Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram represents the curve whose parametric equations are $x = 4t + e^{2t}$, $y = 6t\sin 2t$, where $0 \leq t \leq 1$. Point $P$ lies on the curve and has parameter $p$ and $y$-coordinate $3$.
(a)[1]
Show that $p = \frac{1}{2\sin 2p}$ by starting from the condition on $y$.
(b)[2]
Show by calculation that $p$ lies between $0.5$ and $0.6$.
(c)[3]
Use an iterative formula based on the equation in part (a) to determine $p$ correct to $3$ significant figures. Start with $0.55$ and show the outcome of each iteration to $5$ significant figures.
(d)[5]
Find the gradient of the curve at $P$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Set $y$ equal to $3$ and verify that $p=\frac{1}{2\sin2p}$” …