f(x)=x3+3x2+2x+2f(x) = x^3 + 3x^2 + 2x + 2f(x)=x3+3x2+2x+2
Use the iteration formula xn+1=−(2xn+2xn2+3)\displaystyle x_{n+1} = -\left(\frac{2x_n+2}{x_n^2} + 3\right)xn+1=−(xn22xn+2+3) with x0=−2x_0 = -2x0=−2 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.