Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The values produced by the iterative formula $x_{n+1} = \frac{6 + 8x_n}{8 + x_n^2}$, starting from the initial value $x_1 = 2$, tend towards $\alpha$.
(a)[3]
Use the iteration process to determine the value of $\alpha$ correct to $4$ significant figures. State the result of each step to $6$ significant figures.
(b)[2]
State an equation satisfied by $\alpha$ and then find the exact value of $\alpha$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply iteration correctly at least once” …