The curve C C\,C with the equation y=exy = e^xy=ex meets the line L L\,L with equation y=4xy = 4xy=4x at the point PPP.
Show that the x x\,x coordinate of P P\,P satisfies x=ln(4x)x = \ln(4x)x=ln(4x)
Use the iteration formula xn+1=ln(4xn)x_{n+1} = \ln(4x_n)xn+1=ln(4xn) with x0=2x_0 = 2x0=2 to find, to 3 decimal places, the values of x1,x2 x_1, x_2\,x1,x2 and x3x_3x3.
329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.