Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram depicts the curve $y = 4e^{-2x}$ together with a straight line. The curve intersects the $y$-axis at $P$. The straight line intersects the $y$-axis at the point $(0, 9)$, and its gradient matches the gradient of the curve at $P$. The line cuts the curve at two points, including $Q$, as indicated.
(i)[6]
Show that the $x$-coordinate of $Q$ satisfies $x = \frac{9}{8} - \frac{1}{2}e^{-2x}$.
(ii)[3]
Use an iterative formula derived from the equation in part (i) to determine the $x$-coordinate of $Q$ correct to 3 significant figures. Report each iteration to 5 significant figures.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain a derivative expressed in the form $ke^{-2x}$” …