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**Karrl****Guest**

How do I find taylor series of a function?Is there analysis method,formula or something else?

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,659

hi Karrl

Welcome to the forum.

Yes, there is a formula. Have a look at:

http://en.wikipedia.org/wiki/Taylor_series

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,702

Hi;

What is the function?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Karrl****Guest**

If you meant the first formula,then what are the variables x and a?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,702

Helps a lot to see the particular function you have in mind and what is the point of expansion.

x is the independent variable and a is the point of expansion.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Karrl****Guest**

So for f(p),p=x,and a is any point I want?And will there be taylor series for every function

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,702

Any function that has derivatives that exist at the point of expansion. You can pick any point but that does not mean it will converge.

Sometimes the usual method will not work and you must use another.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Karrl****Guest**

Could you show me an example of taylor series(not the e^x,I know that)and explain how the series is found.

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,702

That is a Taylor series expanded around zero. When it is expanded around zero it is called a Mclaurin series.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Karrl****Guest**

What is the difference in expanding around different points?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,702

The formula or method used is slightly different. Here it is expanded around a and is called a Taylor series.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Karrl****Guest**

So,all values of a will estimate same?if not then what is the best value for a?

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,702

The purpose of the series is to numerically evaluate a value of a function.

An example will make all of it clearer.

Supposing you want to evaluate sin(.1)? Taylor series usually only converge a small distance from the point of expansion. We choose zero because it is close to .1.

Now you plug into x the value that you are looking for. x = .1

The actual value of Sin(.1) is 0.09983341664682815

The approximation is a good one. This is an easy one. In practice they are usually trickier.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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**Karrl****Guest**

So the close a is to x,the better

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,702

Hi;

So the close a is to x,the better

Exactly. The Taylor polynomial has a limited range from the point of expansion.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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