AQA FP3 2013 January — Question 2

Exam BoardAQA
ModuleFP3 (Further Pure Mathematics 3)
Year2013
SessionJanuary
TopicTaylor series
TypeUse binomial with exponential series

2
  1. Write down the expansion of \(\mathrm { e } ^ { 3 x }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 2 }\).
  2. Hence, or otherwise, find the term in \(x ^ { 2 }\) in the expansion, in ascending powers of \(x\), of \(\mathrm { e } ^ { 3 x } ( 1 + 2 x ) ^ { - \frac { 3 } { 2 } }\).
    (4 marks)