MYTUTOR SUBJECT ANSWERS

267 views

What is Taylor Series

 

Technical Definition: A way to approximate (very) smooth functions (for which derivatives up to high orders exist and are continuous)

 

Simple Definition: Taylor series is the infinite sum of all the terms for a specific function which is a very close approximation to the real value of the function. 

Mathematical definition:

f(x) = f(a) + (f'(a)(x-a))/1! + (f''(x)(x-a)2)/2! + (f'''(x)(x-a)3)/3! + ... + 

 

Why do we have an infinite number of terms?:

The more terms we include in our approximated function, the better the approximation to the real value. For a graph this means that it will represent the actual graph function more.

 

Special Case (Maclaurin Series):

Maclaurin series is based of the Taylor Series, but we choose the function to be around origin (value = 0) rather than anywhere else.

 

 

 

Advantage of using Taylor/Maclaurin series

its allows for incredibly accurate approximations of a function (depending on the number of terms included)

Provide for integration and differentiation of functions to arrive at representations of other function

 

Disadvantage of using Taylor/Maclaurin series

some calculations become tedious or the series doesn’t converge quickly

many of the functions are limited to a certain domain given a specific range for convergence (some Taylor series are only valid for a small domain)

Andrew C. GCSE Maths tutor, A Level Maths tutor

1 year ago

Answered by Andrew, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

180 SUBJECT SPECIALISTS

£20 /hr

Charlotte G.

Degree: Medicine (Bachelors) - University College London University

Subjects offered: Maths, Chemistry+ 2 more

Maths
Chemistry
Biology
.BMAT (BioMedical Admissions)

“About Me: I am a medical student at University College London (UCL) who has always had a real passion for science and finding out how things work. I adore Medicine, I very much enjoyed learning about biology, maths and chemistry at s...”

MyTutor guarantee

£26 /hr

George B.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.STEP.

“Third year undergraduate at one of the top universities for Maths. Eager to tutor and help improve your grades.”

£20 /hr

Sean G.

Degree: Biochemistry (Molecular and Cellular) (Bachelors) - Oxford, Worcester College University

Subjects offered: Maths, Further Mathematics + 4 more

Maths
Further Mathematics
Chemistry
Biology
-Personal Statements-
-Oxbridge Preparation-

“Hello, my name is Sean, and I currently read Biochemistry at the University of Oxford. I love science, and greatly enjoy helping others to understand scientific concepts! I can tutor Biology, Chemistry and Maths at GCSE and A-Level, a...”

MyTutor guarantee

About the author

Andrew C.

Currently unavailable: for regular students

Degree: Engineering Mathematics (Masters) - Bristol University

Subjects offered: Maths

Maths

“My name is Andrew, I'm in my second year studying Engineering Mathematics at Bristol. Ever since I was young I really enjoyed learning Maths, it was challenging yet rewarding. Whether you are struggling or just want to get better....”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Given that 4(cosec x)^2 - (cot x)^2 = k, express sec x in terms of k.

Differentiate a^x with respect to x

How to find y-intercept on a graphical calculator

How do I sketch a graph of a polynomial function?

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok