The curve C with the equation y=exy = e^xy=ex meets the line L with equation y=5x−1y = 5x - 1y=5x−1 at the point P.
Show that the x x\,x coordinate of P satisfies x=ln(5x−1)x = \ln(5x - 1)x=ln(5x−1)
Use the iteration formula xn+1=ln(5xn−1)x_{n+1} = \ln(5x_n - 1)xn+1=ln(5xn−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.
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.