f(x)=ex+1+x−8f(x) = e^{x+1} + x - 8f(x)=ex+1+x−8 Let α \alpha\,α denote the root of f(x)=0f(x)=0f(x)=0.
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=ln(8−x)−1x = \ln(8 - x) - 1x=ln(8−x)−1
Use the iteration formula xn+1=ln(8−xn)−1x_{n+1} = \ln(8 - x_n) - 1xn+1=ln(8−xn)−1 with x0=0.5x_0 = 0.5x0=0.5 to find, to 3 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
By choosing a suitable interval, prove that α=0.953\alpha = 0.953α=0.953 to 3 decimal places
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.