The curve C C\,C with equation y=exy = e^xy=ex intersects the line L L\,L with equation y=3x+5y = 3x + 5y=3x+5 at the point QQQ.
Show that the x x\,x coordinate of Q Q\,Q satisfies the equation x=ln(3x+5)x = \ln(3x + 5)x=ln(3x+5).
Using the iterative relation xn+1=ln(3xn+5)x_{n+1} = \ln(3x_n + 5)xn+1=ln(3xn+5) with x0=2.8x_0 = 2.8x0=2.8, calculate the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3, giving each answer to 3 decimal places.
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.
