[H2 MATH] Chapter 9 - Maclaurin Series

SHALYN TAY COPYRIGHTED © A LEVEL H2 MATHEMATICS MACLAURIN’S SERIES

CHAPTER ANALYSIS MASTERY EXAM WEIGHTAGE SHALYN TAY COPYRIGHTED ©

Main Formulas From MF26 SHALYN TAY COPYRIGHTED © Expanding the following term up to and including the term in 𝑥3: 3 + 𝑥 −2 = 3 1 + 𝑥 3 −2 = 1 9 1 + 𝑥 3 −2 = 1 9 [ 1 − 2 𝑥 3 + −2 −3 2! 𝑥 3 2 + −2 −3 −4 3! 𝑥 3 3 + ⋯ = 1 9 − 2 27 𝑥 + 1 27 𝑥2 − 4 243 𝑥3 + ⋯ Range of validity for 𝑥 3 < 1 ⟹ 𝑥 < 3 ⟹ −3 < 𝑥 < 3 Must be 1

Small Angle Approximations SHALYN TAY COPYRIGHTED © For sufficiently small values of 𝜃 , where 𝜃 is in radians (1) sin 𝜃 ≈ 𝜃 (2) cos 𝜃 ≈ 1 − 1 2 𝜃2 (3) tan 𝜃 ≈ 𝜃 Given 𝜃 is sufficiently small for 𝜃4 and higher powers to be neglected, obtain series expansion of sin 2𝜃 1+ cos 3𝜃 sin 2𝜃 1 + cos 2𝜃 ≈ 2𝜃 1 + 1 − 2𝜃 2 2 = 2𝜃 2 − 2𝜃2 = 𝜃 1 − 𝜃2 −1 = 𝜃 1 + 𝜃2 + ⋯ = 𝜃 + 𝜃3

5 For more notes & learning materials, visit: www.overmugged.com ‘A’ levels crash course program IG handle: @overmugged DARRELL ER (COPYRIGHTED) © Join our telegram channel: @overmuggedAlevels Need help? Shalyn Tay (Private tutor with 4 years of experience) 82014166 (Whatsapp) @shalyntay (telegram username) Professionally designed crash courseto help you get a condensed revision before your ‘A’ Levels! Each H2 subject will have 3 crash course modules which will cover their entire H2 syllabus. The 4 hour module focuses on going through key concepts and identifying commonly tested questions! The crash courses modules will begin in June 2021 and last till Oct 2021. Pre-register now on our website and secure your slots!