Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram depicts the curve $y = \frac{\sin 2x}{x + 2}$ for $0 \leq x \leq \frac{1}{2}\pi$. The $x$-coordinate of the highest point $M$ is called $\alpha$.
(i)[4]
Find $\frac{dy}{dx}$ and show that $\alpha$ satisfies the equation $\tan 2x = 2x + 4$.
(ii)[2]
Use a calculation to show that $\alpha$ lies between $0.6$ and $0.7$.
(iii)[3]
Apply the iterative formula $x_{n+1} = \tfrac{1}{2}\tan^{-1}(2x_n + 4)$ to determine $\alpha$ correct to $3$ decimal places. Write down the outcome of each iteration to $5$ decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Some use of the quotient rule, or an equivalent approach, is made” …