14.5 Iteration and numerical methods — Practise

Work through these independently. Choose a method that fits each question. Questions marked H are Higher only.

1. H Use $x_{n+1}=\frac12(x_n+6/x_n)$ with $x_0=2$. Find $x_1$.
2. H Use $x_{n+1}=\frac12(x_n+6/x_n)$ with $x_0=2$. Find $x_2$.
3. H Use $x_{n+1}=\frac12(x_n+6/x_n)$ with $x_0=2$. Find $x_3$ to 3 decimal places.
4. H Use $x_{n+1}=2+1/x_n$ with $x_0=2$. Find $x_2$.
5. H Use $x_{n+1}=3+2/x_n$ with $x_0=2$. Find $x_2$.
6. H Use $x_{n+1}=\frac12(x_n+6/x_n)$ with $x_0=3$. Find $x_2$.
7. H Use $x_{n+1}=x_n/2+1$ with $x_0=8$. Find $x_3$.
8. H Use $x_{n+1}=1+2/x_n$ with $x_0=2$. Find $x_3$.
9. H Which method fits each part, and why? (a) Solve $y=2x+1$ and $y=3x-4$. (b) Use $x_{n+1}=2+1/x_n$ with $x_0=2$ to find $x_2$.