Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The curve in the diagram has parametric equations $x = 3\ln(2t - 3)$, $y = 4t\ln t$. It meets the $y$-axis at the point $A$. At $B$, the gradient of the curve is 12.
(a)[5]
Find the exact gradient of the curve at $A$.
(b)[2]
Show that the parameter value $t$ at $B$ satisfies $t = \frac{9}{1 + \ln t} + \frac{3}{2}$.
(c)[3]
Using the iterative formula based on the equation in part (b), find the value of $t$ at $B$ and give the answer correct to $3$ significant figures. Begin with $5$ and write the outcome of every iteration to $5$ significant figures.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $\dfrac{dx}{dt}=\dfrac{6}{2t-3}$” …