Edexcel FP2 2016 June — Question 6 9 marks

Exam BoardEdexcel
ModuleFP2 (Further Pure Mathematics 2)
Year2016
SessionJune
Marks9
PaperDownload PDF ↗
TopicTaylor series
TypeTaylor series about π/4
DifficultyStandard +0.8 This is a Further Maths question requiring Taylor series expansion about a non-zero point with derivatives of tan x, then application to approximate a specific value. While the technique is standard for FP2, computing successive derivatives of tan x and evaluating at π/4 requires careful algebra, and the substitution in part (b) demands precision. Moderately challenging for Further Maths but not requiring novel insight.
Spec4.08a Maclaurin series: find series for function4.08b Standard Maclaurin series: e^x, sin, cos, ln(1+x), (1+x)^n
6. (a) Find the Taylor series expansion about \(\frac { \pi } { 4 }\) of \(\tan x\) in ascending powers of \(\left( x - \frac { \pi } { 4 } \right)\) up to and including the term in \(\left( x - \frac { \pi } { 4 } \right) ^ { 3 }\).
(b) Deduce that an approximation for \(\tan \frac { 5 \pi } { 12 }\) is \(1 + \frac { \pi } { 3 } + \frac { \pi ^ { 2 } } { 18 } + \frac { \pi ^ { 3 } } { 81 }\) 
6. (a) Find the Taylor series expansion about $\frac { \pi } { 4 }$ of $\tan x$ in ascending powers of $\left( x - \frac { \pi } { 4 } \right)$ up to and including the term in $\left( x - \frac { \pi } { 4 } \right) ^ { 3 }$.\\
(b) Deduce that an approximation for $\tan \frac { 5 \pi } { 12 }$ is $1 + \frac { \pi } { 3 } + \frac { \pi ^ { 2 } } { 18 } + \frac { \pi ^ { 3 } } { 81 }$\\

\hfill \mbox{\textit{Edexcel FP2 2016 Q6 [9]}}
This paper (8 questions)
View full paper
Q1 6 Q2 7 Q3 7 Q4 12 Q5 10 Q6 9 Q7 14 Q8 10