CAIE P3 2002 November — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2002
SessionNovember
TopicGeneralised Binomial Theorem and Partial Fractions

6 Let \(f ( x ) = \frac { 6 + 7 x } { ( 2 - x ) \left( 1 + x ^ { 2 } \right) }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Show that, when \(x\) is sufficiently small for \(x ^ { 4 }\) and higher powers to be neglected, $$f ( x ) = 3 + 5 x - \frac { 1 } { 2 } x ^ { 2 } - \frac { 15 } { 4 } x ^ { 3 }$$