Is there a way to obtain the formula of the Taylor's expression of continuous functions. For example, how can I obtain the Taylor's development of the function without trying to find it by writing down the first derivative, the second one, etc?

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- April 13th 2008, 11:37 AMarbolisTaylor's development question
Is there a way to obtain the formula of the Taylor's expression of continuous functions. For example, how can I obtain the Taylor's development of the function without trying to find it by writing down the first derivative, the second one, etc?

- April 13th 2008, 12:03 PMMathstud28WEll
- April 13th 2008, 12:15 PMarbolis
Ok, thank you. So there's no formal way to obtain these formulas. I must write down the first derivatives and try to guess the nth one. Anyway, I'm having some trouble with the 's one. I would appreciate if you give me the formula (Nod).

- April 13th 2008, 12:24 PMMathstud28No
If you read what I said you could just memorize the power series...and imput the different values...and for I would suggest but am not positve you would use with ...and then apply this Taylor series - Wikipedia, the free encyclopedia look for the one that looks like the one I gave you with the alpha

- April 13th 2008, 12:29 PMbobak

I haven't to time to give a detailed response right now, but this should be enough to get you started.

Firstly when you take your first few derivatives do not attempt the simplify the fractions that may lead to you missing the general formula.

also, for this problem you will need to come up with a formula for the product first n odd numbers, can you see why ?

If you need help with that just ask.

Bobak - April 13th 2008, 12:45 PMarbolisQuote:

also, for this problem you will need to come up with a formula for the product first n odd numbers, can you see why ?

- April 13th 2008, 01:48 PMarbolis
I think I got it. If you replace the (1-2n) in my previous formula by the product of (2i-1), from 0 to n, I think it works! Since I've to go now, I'll check that later.