Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The sketch displays the curves $y = x \cos x$ and $y = \dfrac{k}{x}$, with $k$ a constant, for $0 < x \le \dfrac{\pi}{2}$. These two curves meet at the point for which $x = a$.
(a)[5]
Show that $a$ satisfies the equation $\tan a = \dfrac{2}{a}$.
(b)[3]
Apply the iterative formula $a_{n+1} = \tan^{-1}\!\left( \dfrac{2}{a_n} \right)$ to find $a$ correct to 3 decimal places. Write the outcome of each iteration to 5 decimal places.
(c)[2]
Hence determine the value of $k$ 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: “Differentiate the two equations and set the derivatives equal” …