Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The sketch depicts the curve $y = \frac{\sin x}{x}$ for $0 < x \leq 2\pi$, together with its minimum point $M$.
(i)[4]
Show that the $x$-coordinate of $M$ obeys $x = \tan x$.
(ii)[3]
The iterative formula $x_{n+1} = \tan^{-1}(x_n) + \pi$ may be used to find the $x$-coordinate of $M$. Apply this formula to determine the $x$-coordinate of $M$ correct to $2$ decimal places. Record each iteration to $4$ decimal places.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply a correct quotient rule or product rule” …