Moderate -0.5 This is a multiple-choice question requiring students to either recall or quickly derive the first few terms of standard Maclaurin series. While it's from Further Maths Paper 1, it's essentially pattern matching or straightforward expansion of known series, requiring minimal calculation. The 1-mark allocation confirms it's a quick check rather than extended reasoning.
The first two non-zero terms of the Maclaurin series expansion of \(f(x)\) are \(x\) and \(-\frac{1}{2}x^3\)
Which one of the following could be \(f(x)\)?
Circle your answer.
[1 mark]
\(xe^{\frac{1}{2}x^2}\) \quad \(\frac{1}{2}\sin 2x\) \quad \(x \cos x\) \quad \((1 + x^3)^{-\frac{1}{2}}\)
The first two non-zero terms of the Maclaurin series expansion of $f(x)$ are $x$ and $-\frac{1}{2}x^3$
Which one of the following could be $f(x)$?
Circle your answer.
[1 mark]
$xe^{\frac{1}{2}x^2}$ \quad $\frac{1}{2}\sin 2x$ \quad $x \cos x$ \quad $(1 + x^3)^{-\frac{1}{2}}$
\hfill \mbox{\textit{AQA Further Paper 1 2019 Q2 [1]}}