g(x)=2x3−6x2+3g(x) = 2x^3 - 6x^2 + 3g(x)=2x3−6x2+3
Show that g(x)g(x)g(x) has a root between 0.8 and 0.9
Let α \alpha\,α be the root of g(x)=0g(x) = 0g(x)=0 between 0.8 and 0.9. Show that α=36−2α\displaystyle \alpha = \sqrt{\frac{3}{6-2\alpha}}α=6−2α3.
Use the iteration formula xn+1=36−2xn\displaystyle x_{n+1} = \sqrt{\frac{3}{6-2x_n}}xn+1=6−2xn3 with x0=0.8x_0 = 0.8x0=0.8 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=0.832\alpha = 0.832α=0.832 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.