Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram displays part of the curve with parametric equations $x = 2\ln(t + 2)$, $y = t^3 + 2t + 3$.
(i)[5]
Determine the gradient of the curve at the origin.
(ii(a))[1]
For point $P$ on the curve, the parameter value is $p$. You are told that the gradient at $P$ is $\frac{1}{2}$. Show that $p = \frac{1}{3p^2 + 2} - 2$.
(ii(b))[4]
Using an iterative formula based on the equation in part (a), determine the coordinates of point $P$. Record each iteration to $5$ decimal places and each coordinate of $P$ correct to $2$ decimal places.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $\dfrac{dx}{dt}=\dfrac{2}{t+2}$ together with $\dfrac{dy}{dt}=3t^2+2$” …