(i)[4]
Show that $a = \tfrac{1}{2}\ln(50 + e^{-2a} - 5a)$.
(ii)[3]
Use the iterative formula $a_{n+1} = \tfrac{1}{2}\ln(50 + e^{-2a_n} - 5a_n)$ to determine $a$ correct to $3$ decimal places. Give the result of every iteration to $5$ decimal places.
Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The positive constant $a$ is such that $\int_{-a}^{a} \left(4e^{2x} + 5\right)\,dx = 100$.