f(x)=ex+1+x−5f(x) = e^{x+1} + x - 5f(x)=ex+1+x−5
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=ln(5−x)−1x = \ln(5 - x) - 1x=ln(5−x)−1
Use the iteration formula xn+1=ln(5−xn)−1x_{n+1} = \ln(5 - x_n) - 1xn+1=ln(5−xn)−1 with x0=0.5x_0 = 0.5x0=0.5 to find, to 3 decimal places, the values of x1 x_1\,x1 and x2x_2x2.
By choosing a suitable interval, prove that α=0.503\alpha = 0.503α=0.503 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.