f(x)=x3+2x2+x+1f(x) = x^3 + 2x^2 + x + 1f(x)=x3+2x2+x+1
Use the iteration formula xn+1=−(xn+1xn2+2)\displaystyle x_{n+1} = -\left(\frac{x_n+1}{x_n^2} + 2\right)xn+1=−(xn2xn+1+2) with x0=−1.5x_0 = -1.5x0=−1.5 to find, to 3 decimal places, the values of x1,x2 x_1, x_2\,x1,x2 and x3x_3x3.
321 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.