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=−0.631\alpha = -0.631α=−0.631 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.