Question 4 - A-Level Maths

Exam Board	OCR MEI
Module	Further Pure Core (Further Pure Core)
Year	2023
Session	June
Topic	Taylor series
Type	Maclaurin series for composite exponential/root functions

1. Given that \(\mathrm { f } ( x ) = \sqrt { 1 + 2 x }\), find \(\mathrm { f } ^ { \prime } ( x )\) and \(\mathrm { f } ^ { \prime \prime } ( x )\).
2. Hence, find the first three terms of the Maclaurin series for \(\sqrt { 1 + 2 x }\).
Hence, using a suitable value for \(x\), show that \(\sqrt { 5 } \approx \frac { 143 } { 64 }\).