CAIE P3 2003 June — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2003
SessionJune
TopicGeneralised Binomial Theorem and Partial Fractions

6 Let \(\mathrm { f } ( x ) = \frac { 9 x ^ { 2 } + 4 } { ( 2 x + 1 ) ( x - 2 ) ^ { 2 } }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Show that, when \(x\) is sufficiently small for \(x ^ { 3 }\) and higher powers to be neglected, $$f ( x ) = 1 - x + 5 x ^ { 2 }$$