| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2018 |
| Session | March |
| Marks | 7 |
| Topic | Taylor series |
| Type | Match series to function form |
| Difficulty | Standard +0.8 This requires computing derivatives of a product involving sin x and e^(bx), matching coefficients in a Maclaurin series to find two unknowns, and understanding convergence—multiple conceptual steps beyond routine series expansion. However, it's a standard Further Maths technique with clear structure, not requiring deep insight. |
| Spec | 4.08a Maclaurin series: find series for function4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n |
8 You are given that $\mathrm { f } ( x ) = ( 1 - a \sin x ) \mathrm { e } ^ { b x }$ where $a$ and $b$ are positive constants. The first three terms in the Maclaurin expansion of $\mathrm { f } ( x )$ are $1 + 2 x + \frac { 3 } { 2 } x ^ { 2 }$.\\
(i) Find the value of $a$ and the value of $b$.\\
(ii) Explain if there is any restriction on the value of $x$ in order for the expansion to be valid.
\hfill \mbox{\textit{OCR Further Pure Core 1 2018 Q8 [7]}}