hello all

i have a bit problem with finding the taylor polynomial for a composed function.

if anyone can help me find the taylor polynomial for the function f(x) = e^sin(x) and how i would appriciate it alot

thanks!

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- Jul 17th 2012, 12:36 AMdorubintaylor polynomial for composition
hello all

i have a bit problem with finding the taylor polynomial for a composed function.

if anyone can help me find the taylor polynomial for the function f(x) = e^sin(x) and how i would appriciate it alot

thanks! - Jul 17th 2012, 01:57 AMgirdavRe: taylor polynomial for composition
Which degree does the Taylor polynomial needs to have?

- Jul 17th 2012, 02:07 AMdorubinRe: taylor polynomial for composition
doesnt matter, i want to know how is it done. lets say up to 5'th degree around 0

- Jul 17th 2012, 02:10 AMgirdavRe: taylor polynomial for composition
It's in general not easy to find the Taylor expansion of the composition of two function. There exists a formula, due to Faà di Bruno.

- Jul 17th 2012, 02:20 AMProve ItRe: taylor polynomial for composition
You can always do it the long way. Let .

We know that , so let and we find .

Differentiate both sides and we find

We know , so let and we find .

Differentiate both sides and we have

We know that so let and we find .

Follow this process to find as many terms as you need. I doubt that there will be a pattern. - Jul 17th 2012, 05:13 AMdorubinRe: taylor polynomial for composition
thanks guys