f(x)=e2−x+3x−12f(x) = e^{2-x} + 3x - 12f(x)=e2−x+3x−12
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=2−ln(12−3x)x = 2 - \ln(12 - 3x)x=2−ln(12−3x)
Use the iteration formula xn+1=2−ln(12−3xn)x_{n+1} = 2 - \ln(12 - 3x_n)xn+1=2−ln(12−3xn) with x0=1.0x_0 = 1.0x0=1.0 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=−0.632\alpha = -0.632α=−0.632 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.
