The curve C has the equation y=(15−x)lnxy = (15 - x) \ln xy=(15−x)lnx, x>0x > 0x>0
Use the iteration formula xn+1=151+lnxn\displaystyle x_{n+1} = \frac{15}{1 + \ln x_n}xn+1=1+lnxn15 with x0=5.5x_0 = 5.5x0=5.5 to find, to 3 decimal places, the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
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.