f(x)=x3−3x2−2x+5f(x) = x^3 - 3x^2 - 2x + 5f(x)=x3−3x2−2x+5
Show that f(x)f(x)f(x) has a root between 3.1 and 3.2
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=3+2x−5x2\displaystyle x = 3 + \frac{2x-5}{x^2}x=3+x22x−5
Use the iteration formula xn+1=3+2xn−5xn2\displaystyle x_{n+1} = 3 + \frac{2x_n-5}{x_n^2}xn+1=3+xn22xn−5 with x0=3.1x_0 = 3.1x0=3.1 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=3.128\alpha = 3.128α=3.128 to 3 decimal places
125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.