| Exam Board | OCR |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2008 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Taylor series |
| Type | Maclaurin series for ln(trigonometric expressions) |
| Difficulty | Standard +0.3 This is a straightforward application of Maclaurin series requiring differentiation of ln(1+cos x), evaluation at x=0, and substitution into the standard formula. The derivatives are routine (chain rule with standard trig derivatives), and finding two non-zero terms requires minimal algebraic manipulation. While it's Further Maths content, it's a standard textbook exercise with no conceptual challenges. |
| Spec | 4.08a Maclaurin series: find series for function4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
1 It is given that $\mathrm { f } ( x ) = \ln ( 1 + \cos x )$.\\
(i) Find the exact values of $f ( 0 ) , f ^ { \prime } ( 0 )$ and $f ^ { \prime \prime } ( 0 )$.\\
(ii) Hence find the first two non-zero terms of the Maclaurin series for $\mathrm { f } ( x )$.
\hfill \mbox{\textit{OCR FP2 2008 Q1 [6]}}