The curve C C\,C with equation y=exy = e^xy=ex meets the line L L\,L with equation y=2x+10y = 2x + 10y=2x+10 at the point RRR.
Show that the x x\,x coordinate of R R\,R satisfies x=ln(2x+10)x = \ln(2x + 10)x=ln(2x+10).
Use the iteration formula xn+1=ln(2xn+10)x_{n+1} = \ln(2x_n + 10)xn+1=ln(2xn+10) with x0=3x_0 = 3x0=3 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.
