CAIE P3 2014 November — Question 9

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2014
SessionNovember
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TopicPartial Fractions
9 Let \(\mathrm { f } ( x ) = \frac { x ^ { 2 } - 8 x + 9 } { ( 1 - x ) ( 2 - x ) ^ { 2 } }\).
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Hence obtain the expansion of \(\mathrm { f } ( x )\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\).
9 Let $\mathrm { f } ( x ) = \frac { x ^ { 2 } - 8 x + 9 } { ( 1 - x ) ( 2 - x ) ^ { 2 } }$.\\
(i) Express $\mathrm { f } ( x )$ in partial fractions.\\
(ii) Hence obtain the expansion of $\mathrm { f } ( x )$ in ascending powers of $x$, up to and including the term in $x ^ { 2 }$.

\hfill \mbox{\textit{CAIE P3 2014 Q9}}
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