Question 2 - A-Level Maths

Exam Board	OCR
Module	Further Pure Core 1 (Further Pure Core 1)
Year	2021
Session	November
Topic	Taylor series
Type	Maclaurin series of shifted function

2 You are given that \(\mathrm { f } ( x ) = \tan ^ { - 1 } ( 1 + x )\).

1. Find the value of \(f ( 0 )\).
2. Determine the value of \(f ^ { \prime } ( 0 )\).
3. Show that \(f ^ { \prime \prime } ( 0 ) = - \frac { 1 } { 2 }\).
Hence find the Maclaurin series for \(\mathrm { f } ( x )\) up to and including the term in \(x ^ { 2 }\).