Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The graph displays the curves $y = e^{2x-3}$ and $y = 2 \ln x$. At $x = a$, the tangents drawn to the two curves are parallel.
(a(i))[3]
Show that $a$ obeys the equation $a = \tfrac{1}{2}(3 - \ln a)$.
(a(ii))[2]
Use calculation to confirm that this equation has a root in the interval between $1$ and $2$.
(a(iii))[3]
Apply the iterative formula $a_{n+1} = \tfrac{1}{2}(3 - \ln a_n)$ to find $a$ correct to $2$ decimal places, displaying each iteration to $4$ decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State the correct derivatives of $2e^{2x-3}$ and $2/x$” …