| Exam Board | OCR |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Taylor series |
| Type | Maclaurin series for composite exponential/root functions |
| Difficulty | Standard +0.3 This is a straightforward Further Maths question requiring standard differentiation of a composite exponential function and direct application of the Maclaurin series formula. While it involves chain rule and product rule, the derivatives at x=0 simplify nicely (sin 0 = 0, cos 0 = 1), making this a routine textbook exercise with no conceptual challenges beyond knowing the standard procedure. |
| Spec | 1.07j Differentiate exponentials: e^(kx) and a^(kx)1.07k Differentiate trig: sin(kx), cos(kx), tan(kx)1.07r Chain rule: dy/dx = dy/du * du/dx and connected rates4.08a Maclaurin series: find series for function |
3 (i) Given that $\mathrm { f } ( x ) = \mathrm { e } ^ { \sin x }$, find $\mathrm { f } ^ { \prime } ( 0 )$ and $\mathrm { f } ^ { \prime \prime } ( 0 )$.\\
(ii) Hence find the first three terms of the Maclaurin series for $\mathrm { f } ( x )$.
\hfill \mbox{\textit{OCR FP2 2009 Q3 [6]}}