| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2013 |
| Session | November |
| Topic | Fixed Point Iteration |
| Type | Show root in interval |
| Difficulty | Moderate -0.3 Part (i) is a standard 'show root in interval' question requiring simple substitution into f(x) and sign change verification. Part (ii) is routine fixed-point iteration with a given formula—just repeated calculation until convergence. Both parts are mechanical with no problem-solving required, making this slightly easier than average. |
| Spec | 1.09a Sign change methods: locate roots1.09c Simple iterative methods: x_{n+1} = g(x_n), cobweb and staircase diagrams |
3 (i) Show that the equation $x ^ { 2 } - \ln x - 2 = 0$ has a solution between $x = 1$ and $x = 2$.\\
(ii) Find an approximation to that solution using the iteration $x _ { n + 1 } = \sqrt { 2 + \ln x _ { n } }$, giving your answer correct to 2 decimal places.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2013 Q3}}