Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
You are told that $\int_{-a}^{2a} 4e^{-2x}\,dx = 25$, with $a$ a positive constant.
(i)[4]
Show, by working, that $a = \frac{1}{2}\ln\left(12.5 + e^{-4a}\right)$.
(ii)[2]
Using the equation from part (i), show by calculation that $1.0 \le a \le 1.5$.
(iii)[3]
Apply an iterative formula based on the equation in part (i) to determine the value of $a$ correct to 4 significant figures. Record the outcome of each iteration to 6 significant figures.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Integrate and get $-2\mathrm e^{-2x}$” …