f(x)=ln(x+4)−x+1f(x) = \ln(x+4) - x + 1f(x)=ln(x+4)−x+1
Show that the equation f(x)=0f(x) = 0f(x)=0 can be written in the form x=ln(x+4)+1x = \ln(x+4) + 1x=ln(x+4)+1
Use the iteration formula xn+1=ln(xn+4)+1x_{n+1} = \ln(x_n + 4) + 1xn+1=ln(xn+4)+1 with x0=2.5x_0 = 2.5x0=2.5 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=2.937\alpha = 2.937α=2.937 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.