Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
For the curve defined by $y = 5e^{2x} - 8x^2 - 20$, there is only one point where it intersects the $x$-axis. The coordinates of this point are $(p, 0)$.
(i)[2]
Show that the value $p$ satisfies the equation $x = \frac{1}{2}\ln(1.6x^2 + 4)$.
(ii)[2]
Show by calculation that $0.75 \le p \le 0.85$.
(iii)[3]
Use the iterative method based on the equation in part (i) to determine the value of $p$ correct to 5 significant figures. Record the outcome of each iteration to 7 significant figures.
(iv)[3]
Find the gradient of the curve at the point $(p, 0)$, using the point given.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Rearrange the equation to at least the stage $2x=\ln(\ldots)$” …