Moderate -0.8 This is a straightforward recall question testing knowledge of standard Maclaurin series. Students need only remember that ln(1+x) = x - x²/2 + x³/3 - x⁴/4 + ... and recognize the fourth term is -x⁴/4 = -1/4! × x⁴ (noting the pattern). While it's Further Maths content, it requires minimal calculation and no problem-solving—just pattern recognition of memorized series.
Which of the following functions has the fourth term \(-\frac{1}{720}x^6\) in its Maclaurin series expansion?
Circle your answer.
[1 mark]
\(\sin x\) \(\qquad\) \(\cos x\) \(\qquad\) \(e^x\) \(\qquad\) \(\ln(1 + x)\)
Which of the following functions has the fourth term $-\frac{1}{720}x^6$ in its Maclaurin series expansion?
Circle your answer.
[1 mark]
$\sin x$ $\qquad$ $\cos x$ $\qquad$ $e^x$ $\qquad$ $\ln(1 + x)$
\hfill \mbox{\textit{AQA Further AS Paper 1 2018 Q3 [1]}}