The curve C C\,C with equation y=exy = e^xy=ex meets the line L L\,L with equation y=5x−1y = 5x - 1y=5x−1 at the point PPP.
Show that the xxx-coordinate of P P\,P satisfies x=ln(5x−1)x = \ln(5x - 1)x=ln(5x−1).
Use the iteration formula
xn+1=ln(5xn−1)x_{n+1} = \ln(5x_n - 1)xn+1=ln(5xn−1)
with x0=2.5x_0 = 2.5x0=2.5 to find, to three decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.