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 OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.