The curve C with the equation y=exy = e^xy=ex meets the line L with equation y=e2x−e2y = e^2x - e^2y=e2x−e2 at the point P.
Show that the x x\,x coordinate of P satisfies x=ln(e2x−e2)x = \ln(e^2x - e^2)x=ln(e2x−e2)
Use the iteration formula xn+1=ln(e2xn−e2)x_{n+1} = \ln(e^2x_n - e^2)xn+1=ln(e2xn−e2) with x3=2.1x_3 = 2.1x3=2.1 to find, to 3 decimal places, the values of x0x_0x0, x1 x_1\,x1 and x2x_2x2.
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.