OCR FP2 2008 January — Question 1

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2008
SessionJanuary
TopicTaylor series
TypeMaclaurin series for ln(trigonometric expressions)
1 It is given that \(\mathrm { f } ( x ) = \ln ( 1 + \cos x )\).
  1. Find the exact values of \(f ( 0 ) , f ^ { \prime } ( 0 )\) and \(f ^ { \prime \prime } ( 0 )\).
  2. Hence find the first two non-zero terms of the Maclaurin series for \(\mathrm { f } ( x )\).
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