OCR FP2 2012 January — Question 1

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2012
SessionJanuary
TopicTaylor series
TypeMaclaurin series for ln(trigonometric expressions)

1 Given that \(\mathrm { f } ( x ) = \ln ( \cos 3 x )\), find \(\mathrm { f } ^ { \prime } ( 0 )\) and \(\mathrm { f } ^ { \prime \prime } ( 0 )\). Hence show that the first term in the Maclaurin series for \(\mathrm { f } ( x )\) is \(a x ^ { 2 }\), where the value of \(a\) is to be found.