OCR FP2 2007 January — Question 1

Exam BoardOCR
ModuleFP2 (Further Pure Mathematics 2)
Year2007
SessionJanuary
TopicTaylor series
TypeMaclaurin series for ln(a+bx)

1 It is given that \(\mathrm { f } ( x ) = \ln ( 3 + x )\).
  1. Find the exact values of \(f ( 0 )\) and \(f ^ { \prime } ( 0 )\), and show that \(f ^ { \prime \prime } ( 0 ) = - \frac { 1 } { 9 }\).
  2. Hence write down the first three terms of the Maclaurin series for \(\mathrm { f } ( x )\), given that \(- 3 < x \leqslant 3\).