Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The values produced by the iterative formula $x_{n+1} = \frac{6 + 8x_n}{8 + x_n^2}$ with starting value $x_1 = 2$ tend to $\alpha$.
(a)[3]
Apply the iterative formula to determine the value of $\alpha$ correct to $4$ significant figures. Write down the outcome of each iteration to $6$ significant figures.
(b)[2]
State an equation that $\alpha$ satisfies 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: “Carry out the iteration correctly at least once” …