The curve C with the equation y=exy = e^xy=ex meets the line L with equation y=5x−1y = 5x - 1y=5x−1 at the point P.
Show that the x x\,x coordinate of 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 3 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
