The curve C C\,C with equation y=exy = e^xy=ex intersects the line L L\,L with equation y=3x+5y = 3x + 5y=3x+5 at the point QQQ.
Show that the x x\,x coordinate of Q Q\,Q satisfies the equation x=ln(3x+5)x = \ln(3x + 5)x=ln(3x+5).
Using the iterative relation xn+1=ln(3xn+5)x_{n+1} = \ln(3x_n + 5)xn+1=ln(3xn+5) with x0=2.8x_0 = 2.8x0=2.8, calculate the values of x1x_1x1, x2 x_2\,x2 and x3x_3x3, giving each answer 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.