f(x)=ex+2+x−10f(x) = e^{x+2} + x - 10f(x)=ex+2+x−10
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=ln(10−x)−2x = \ln(10 - x) - 2x=ln(10−x)−2
Use the iteration formula xn+1=ln(10−xn)−2x_{n+1} = \ln(10 - x_n) - 2xn+1=ln(10−xn)−2 with x0=0.5x_0 = 0.5x0=0.5 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=0.275\alpha = 0.275α=0.275 to 3 decimal places
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.