3.7 Numerical methods (A-level only)

The curve C with the equation $y = e^x$ meets the line L with equation $y = 5 x - 1$ at the point P.

Show that the $x\,$ coordinate of P satisfies $\ln(5x - 1)$

[2]

Use the iteration formula $x_{n+1} = \ln(5x_n - 1)$ with $x_0 = 2.5$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

3.7 Numerical methods (A-level only) Questions

The curve C with the equation $y = e^x$ meets the line L with equation $y = 5 x - 1$ at the point P.

Show that the $x\,$ coordinate of P satisfies $\ln(5x - 1)$

[2]

Use the iteration formula $x_{n+1} = \ln(5x_n - 1)$ with $x_0 = 2.5$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]