f(x) =
f(0)+xf'(0)+\frac{x^2}{2!}f''(0)+\frac{x^3}{3!}f^{(3)}(0)+...+\frac{x^r}{r!}f^{(r)}(0)+...+\frac{x^n}{n!}f^{(n)}(0)
Summary/Background

The graphs shows approximations to \sin x for n = 0, 1, 2 and 3.

Maclaurin was a Scottish mathematican who published the first systematic exposition of Newton's methods, written as a reply to Berkeley's attack on the calculus for its lack of rigorous foundations.
Software/Applets used on this page
This question appears in the following syllabi:
Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|
AP Calculus BC (USA) | 5 | Maclaurin and Taylor Series | Maclaurin series | - |
AQA A-Level (UK - Pre-2017) | FP3 | Maclaurin and Taylor Series | Maclaurin series | - |
AQA A2 Further Maths 2017 | Pure Maths | Further Sequences and Series | Further Maclaurin Series | - |
AQA AS Further Maths 2017 | Pure Maths | Sequences, Series and Proof | Maclaurin Series | - |
AQA AS/A2 Further Maths 2017 | Pure Maths | Sequences, Series and Proof | Maclaurin Series | - |
CCEA A-Level (NI) | FP2 | Maclaurin and Taylor Series | Maclaurin series | - |
Edexcel A-Level (UK - Pre-2017) | FP2 | Maclaurin and Taylor Series | Maclaurin series | - |
Edexcel A2 Further Maths 2017 | Core Pure Maths | Further Series | Maclaurin Series | - |
Edexcel AS/A2 Further Maths 2017 | Core Pure Maths | Further Series | Maclaurin Series | - |
I.B. Higher Level | 9 | Maclaurin and Taylor Series | Maclaurin series | - |
Methods (UK) | M10 | Maclaurin and Taylor Series | Maclaurin series | - |
OCR A-Level (UK - Pre-2017) | FP2 | Maclaurin and Taylor Series | Maclaurin series | - |
OCR A2 Further Maths 2017 | Pure Core | Calculus | Maclaurin Series | - |
OCR MEI A2 Further Maths 2017 | Core Pure B | Series | Maclaurin Series | - |
OCR-MEI A-Level (UK - Pre-2017) | FP2 | Maclaurin and Taylor Series | Maclaurin series | - |
Scottish Advanced Highers | M3 | Maclaurin and Taylor Series | Maclaurin series | - |
Scottish (Highers + Advanced) | AM3 | Maclaurin and Taylor Series | Maclaurin series | - |
Universal (all site questions) | M | Maclaurin and Taylor Series | Maclaurin series | - |
WJEC A-Level (Wales) | FP3 | Maclaurin and Taylor Series | Maclaurin series | - |