Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
A curve is described by $y = \dfrac{x}{\cos^2 x}$, for $0 < x < \tfrac{1}{2}\pi$. At the point where $x = a$, the tangent to the curve has gradient $12$.
(a)[3]
Hence show that $a = \cos^{-1}\!\left(\sqrt[3]{\dfrac{\cos a + 2a\sin a}{12}}\right).$
(b)[2]
Use calculation to verify that $a$ lies between $0.9$ and $1$.
(c)[3]
Apply an iterative formula derived from part (a) to find $a$ correct to $2$ decimal places. Present each iterate to $4$ decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the correct product rule or quotient rule” …