Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
Let the x-coordinates of the intersection points be represented by $\alpha$ and $\beta$, with $\alpha < \beta$.
(a)[2]
On one set of axes, sketch the graphs of $y = |2x - 3|$ and $y = \ln(x + 1)$.
(b)[1]
Prove that $\alpha = 1.5 - 0.5\ln(\alpha + 1)$.
(c)[3]
Apply an iterative formula derived from the equation in part (b) to determine $\alpha$ correct to 3 significant figures. Record each iterate to 5 significant figures.
(d)[2]
Show by calculation that $2.055 < \beta < 2.065$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Draw an increasing curve for $y=\ln(x+1)$ that passes through the origin” …