Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The graph depicts the curve $y = e^{-\frac{1}{2}x^2}\sqrt{(1 + 2x^2)}$ for $x \geq 0$, together with its highest point $M$.
(a(i))[4]
Find the exact $x$-coordinate of $M$.
(a(ii))[3]
The iteration $x_{n+1} = \sqrt{\ln(4 + 8x_n^2)}$, starting from $x_1 = 2$, approaches a value $\alpha$. State an equation that $\alpha$ satisfies and so show that $\alpha$ is the $x$-coordinate of a point on the curve with $y = 0.5$.
(a(iii))[3]
Use the iteration rule to determine $\alpha$ correct to $2$ decimal places, and give every iterated value to $4$ decimal places.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the correct product/quotient rule and chain rule.” …