3.8.2 Numerical Methods (A-level only)

The curve $C\,$ with equation $y = e^x$ meets the line $L\,$ with equation $y = 4 x + 3$ at the point $P$ .

a.

Show that the $x\,$ coordinate of $P\,$ satisfies $\ln(4x + 3)$ .

[2]

b.

Use the iteration formula $x_{n+1} = \ln(4x_n + 3)$ with $x_0 = 2$ 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 $y = 4 x + 3$ at the point $P$ .

a.

Show that the $x\,$ coordinate of $P\,$ satisfies $\ln(4x + 3)$ .

[2]

b.

Use the iteration formula $x_{n+1} = \ln(4x_n + 3)$ with $x_0 = 2$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .

[3]

3.8.2 Numerical Methods (A-level only) Questions