N2010 P1 Q2
N2010 P1 Q2
Junior College 2
6 marks
- Find the first three terms of the Maclaurin series for \(\mathrm e^x(1+\sin2x)\). [You may use standard results given in the List of Formulae (MF15).][3]
- It is given that the first two terms of this series are equal to the first two terms in the series expansion, in ascending powers of \(x\), of \((1+\frac43x)^n\). Find \(n\) and show that the third terms in each of the series are equal.[3]
Solution:
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Answer:(i) \(1+3x+\frac52x^2\). (ii) \(n=9/4\); both third terms are \(\frac52x^2\).
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