Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The curve $y = \frac{\ln x}{x + 1}$ has a single stationary point.
(i)[5]
Show that the $x$-coordinate of this point obeys the equation $x = \frac{x + 1}{\ln x}$, and that this $x$-coordinate is between $3$ and $4$.
(ii)[3]
Use the iterative formula $x_{n+1} = \frac{x_n + 1}{\ln x_n}$ to find the $x$-coordinate correct to $2$ decimal places. Record the outcome of 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: “Use the appropriate quotient or product rule” …