f(x)=ex−1+x−4f(x) = e^{x-1} + x - 4f(x)=ex−1+x−4
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=ln(4−x)+1x = \ln(4 - x) + 1x=ln(4−x)+1
Use the iteration formula xn+1=ln(4−xn)+1x_{n+1} = \ln(4 - x_n) + 1xn+1=ln(4−xn)+1 with x0=1.5x_0 = 1.5x0=1.5 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=1.792\alpha = 1.792α=1.792 to 3 decimal places.
80 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.