1.10.3 Fixed point iteration (A-level only)

The curve $C\,$ with equation $y = e^x$ meets the line $L\,$ with equation $y = 2 x + 10$ at the point $R$ .

a.

Show that the $x\,$ coordinate of $R\,$ satisfies $\ln(2x + 10)$ .

[2]

b.

Use the iteration formula $x_{n+1} = \ln(2x_n + 10)$ with $x_0 = 3$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

The curve $C\,$ with equation $y = e^x$ meets the line $L\,$ with equation $y = 2 x + 10$ at the point $R$ .

a.

Show that the $x\,$ coordinate of $R\,$ satisfies $\ln(2x + 10)$ .

[2]

b.

Use the iteration formula $x_{n+1} = \ln(2x_n + 10)$ with $x_0 = 3$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

1.10.3 Fixed point iteration (A-level only) Questions