N2007 P2 Q3

N2007 P2 Q3

Junior College 2
11 marks
  1. By successively differentiating \((1+x)^n\), find Maclaurin’s series for \((1+x)^n\), up to and including the term in \(x^3\).[4]
  2. Obtain the expansion of \((4-x)^{3/2}(1+2x^2)^{3/2}\) up to and including the term in \(x^3\).[5]
  3. Find the set of values of \(x\) for which the expansion in part (ii) is valid.[2]

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Answer:(ii) \(8-3x+387x^2/16-1151x^3/128+\cdots\). (iii) \(|x|<1/\sqrt2\).

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