f(x)=ex+2+x−9f(x) = e^{x+2} + x - 9f(x)=ex+2+x−9
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=ln(9−x)−2x = \ln(9 - x) - 2x=ln(9−x)−2
Use the iteration formula xn+1=ln(9−xn)−2x_{n+1} = \ln(9 - x_n) - 2xn+1=ln(9−xn)−2 with x0=0.5x_0 = 0.5x0=0.5 to find, to 3 decimal places, the values of x1,x2 x_1, x_2\,x1,x2 and x3x_3x3.
The root of f(x)=0f(x) = 0f(x)=0 is α\alphaα. By choosing a suitable interval, prove that α=0.177\alpha = 0.177α=0.177 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.