OCR Further Pure Core 1 2018 December — Question 3

Exam BoardOCR
ModuleFurther Pure Core 1 (Further Pure Core 1)
Year2018
SessionDecember
TopicTaylor series
TypeMaclaurin series for ln(a+bx)

3 You are given that \(\mathrm { f } ( x ) = \ln ( 2 + x )\).
  1. Determine the exact value of \(\mathrm { f } ^ { \prime } ( 0 )\).
  2. Show that \(\mathrm { f } ^ { \prime \prime } ( 0 ) = - \frac { 1 } { 4 }\).
  3. Hence write down the first three terms of the Maclaurin series for \(\mathrm { f } ( x )\).