Figure 1 below shows the graph of y=ln(4x+3)y = \ln(4x + 3)y=ln(4x+3) and the graph of y=xy = xy=x.
Show that the equation ln(4x+3)=x\ln(4x + 3) = xln(4x+3)=x has a root between 2 and 3.
Use Figure 1, starting with x1=2x_1 = 2x1=2, to determine whether the iteration formula
xn+1=ln(4xn+3)x_{n+1} = \ln(4x_n + 3)xn+1=ln(4xn+3)
can be used to find an approximation for this root. Justify your answer.
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.