Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram illustrates the curve $y = x^2 \cos 2x$ for $0 \leq x \leq \frac{1}{4}\pi$. On the curve, the highest point is $M$, where $x = p$.
(i)[3]
Show that $p$ is a solution of the equation $p = \frac{1}{2} \tan^{-1}\left(\frac{1}{p}\right)$.
(ii)[3]
Use the iterative formula $p_{n+1} = \frac{1}{2} \tan^{-1}\left(\frac{1}{p_n}\right)$ to find $p$ correct to 2 decimal places. Record the outcome of every iteration to 4 decimal places.
(iii)[5]
Find, showing all necessary working, the exact area of the region enclosed by the curve and the $x$-axis.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the product rule correctly” …