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July 10th, 2018, 10:04 AM   #1
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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
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July 10th, 2018, 10:43 AM   #2
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Originally Posted by Mathmatizer View Post
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
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Last edited by skipjack; July 10th, 2018 at 12:12 PM.
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July 10th, 2018, 10:46 AM   #3
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Thanks, I was able to solve it!
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