2 It is given that \(\mathrm { f } ( x ) = \tan ^ { - 1 } ( 1 + x )\).
- Find \(\mathrm { f } ( 0 )\) and \(\mathrm { f } ^ { \prime } ( 0 )\), and show that \(\mathrm { f } ^ { \prime \prime } ( 0 ) = - \frac { 1 } { 2 }\).
- Hence find the Maclaurin series for \(\mathrm { f } ( x )\) up to and including the term in \(x ^ { 2 }\).