The curve C with the equation y=exy = e^xy=ex meets the line L with equation y=x+1y = x + 1y=x+1 at the point P.
Show that the x x\,x coordinate of P satisfies x=ln(x+1)x = \ln(x + 1)x=ln(x+1)
Use the iteration formula xn+1=ln(xn+1)x_{n+1} = \ln(x_n + 1)xn+1=ln(xn+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.
321 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.