Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The sketch displays the curves $y = 4\cos\frac{1}{2}x$ and $y = \frac{1}{4 - x}$, for $0 \le x < 4$. At the point where $x = a$, the tangents drawn to the two curves are at right angles.
(i)[4]
Show that $a = 4 - \sqrt{2\sin\frac{1}{2}a}$.
(ii)[2]
Check by calculation that $a$ is between $2$ and $3$.
(iii)[3]
Apply an iterative formula derived from the equation in part (i) to find $a$ correct to $3$ decimal places. Present each iterative value 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: “State one correct derivative at least” …