Figure 1 below shows the graphs of $\ln(5 - x)$ and $y = x$ . The curve meets the line at a single point, where $\alpha$ .

Figure for question 8

Show that $\alpha < 2$ .

Use Figure 1, starting with $x_1 = 2$ , to determine whether the iteration formula

$x_{n+1} = \ln(5 - x_n)$

can be used to find an approximation for $α\alpha$ . Justify your answer.

Use the iteration formula with $x_1 = 2$ to find $x_2$ , $x_3\,$ and $x_4$ , giving your answers to four decimal places.

On Figure 1, draw a cobweb or staircase diagram to show how the convergence takes place.

Figure 1 below shows the graphs of $\ln(5 - x)$ and $y = x$ . The curve meets the line at a single point, where $\alpha$ .

Figure for question 8

Show that $\alpha < 2$ .

Use Figure 1, starting with $x_1 = 2$ , to determine whether the iteration formula

$x_{n+1} = \ln(5 - x_n)$

can be used to find an approximation for $α\alpha$ . Justify your answer.

Use the iteration formula with $x_1 = 2$ to find $x_2$ , $x_3\,$ and $x_4$ , giving your answers to four decimal places.

On Figure 1, draw a cobweb or staircase diagram to show how the convergence takes place.

1.9 Numerical Methods (A-level only)

1.9 Numerical Methods (A-level only) Questions