Show that the equation f(x)=0f(x) = 0f(x)=0 can be written as
x=(2x+12). x = \sqrt{\left(\frac{2}{x} + \frac{1}{2}\right)}. x=(x2+21).The equation 2x3−x−4=02x^3 - x - 4 = 02x3−x−4=0 has a root between 1.35 and 1.4. Use the iteration formula
xn+1=(2xn+12), x_{n+1} = \sqrt{\left(\frac{2}{x_n} + \frac{1}{2}\right)}, xn+1=(xn2+21),with x0=1.35x_0 = 1.35x0=1.35, to find, to 2 decimal places, the value of x1x_1x1, x2 x_2\,x2 and x3x_3x3.
The only real root of f(x)=0f(x) = 0f(x)=0 is α\alphaα. By choosing a suitable interval, prove that α=1.392\alpha = 1.392α=1.392, to 3 decimal places.
7 exam-style questions on Edexcel A Level Old Maths Numerical Methods. Each one has a worked solution and a mark scheme showing where the marks go.