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 July 10th, 2018, 09:04 AM #1 Newbie   Joined: Oct 2017 From: Here Posts: 19 Thanks: 0 Taylor series of multiplied functions I am having hard times trying to write the Taylor series of: x*(cos(2pi*x)) to 2nd order around the point a=1 What do I need to do? thanks
July 10th, 2018, 09:43 AM   #2
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 Originally Posted by Mathmatizer I am having hard times trying to write the Taylor series of: x*(cos(2pi*x)) to 2nd order around the point a=1 What do I need to do? thanks
There are two ways to do this. First, simply find the Taylor series for $\displaystyle x~\cos( 2 \pi x) \approx 1 + (x - 1) + 2 \pi (x - 1)^2 + \text{ ... }$

The other way is to find the Taylor series of each individual function:
$\displaystyle x = 1 + (x - 1)$

$\displaystyle \cos( 2 \pi x) \approx 1 + 2 \pi^2 (x - 1)^2 + \text{ ... }$

Multiply the two expressions and discard the term in (x - 1)^3 and you'll get the expression for the whole thing given above.

-Dan

Last edited by skipjack; July 10th, 2018 at 11:12 AM.

 July 10th, 2018, 09:46 AM #3 Newbie   Joined: Oct 2017 From: Here Posts: 19 Thanks: 0 Thanks, I was able to solve it!

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