The curve C C\,C with equation y=exy = e^xy=ex meets the line L L\,L with equation y=4x+3y = 4x + 3y=4x+3 at the point PPP.
Show that the x x\,x coordinate of P P\,P satisfies x=ln(4x+3)x = \ln(4x + 3)x=ln(4x+3).
Use the iteration formula xn+1=ln(4xn+3)x_{n+1} = \ln(4x_n + 3)xn+1=ln(4xn+3) with x0=2x_0 = 2x0=2 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.
