(i)[3]
Apply this iterative formula to determine $\alpha$ correct to 3 decimal places. Record the outcome of every iteration to 5 decimal places.
(ii)[2]
State an equation satisfied by $\alpha$ and then determine the exact value of $\alpha$.
Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The values generated by the iterative formula $x_{n+1} = \sqrt{\tfrac{1}{2}x_n^2 + 4x_n^{-3}}$, starting from $x_1 = 1.5$, approach $\alpha$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the iterative formula correctly on at least one occasion” …
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