Question 8 - A-Level Maths

Exam Board	AQA
Module	Further Paper 2 (Further Paper 2)
Year	2022
Session	June
Topic	Taylor series
Type	Maclaurin series for products/secant

The function f is defined as $\mathrm { f } ( x ) = \sec x$ 8
1. Show that $\mathrm { f } ^ { ( 4 ) } ( 0 ) = 5$
  8
(ii) Hence find the first three non-zero terms of the Maclaurin series for $\mathrm { f } ( x ) = \sec x$
8
Prove that $$\lim _ { x \rightarrow 0 } \left( \frac { \sec x - \cosh x } { x ^ { 4 } } \right) = \frac { 1 } { 6 }$$