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
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
