Math Is Fun Forum

Natkirky

Member

Registered: 2006-10-17

Posts: 21

Maclaurin Series

Hi,

I am doing first year uni maths and i was wondering if someone could please help with the following question?

By multiplying together known Maclaurin Series obtain the expansion of (cos2x)log(1+x²) up to term x^6.

I have found co2x to be 1- 2x² + 2/3x^4 - 4/45x^6 + ...

and log(1+x²) to be tan-¹x = x - 1/3x³ + 1/5x^5 +...

By multiplying these values together I am not getting the correct answer and I don't have a clue where I'm going wrong.  The solution I have is x² - 5/2x^4 + 2x^6.

I would be grateful for any help or corrections if I am doing this completely wrong.

Thank you.

DLF24

Member

Registered: 2011-02-11

Posts: 3

Re: Maclaurin Series

Your series for log(1+x^2) is incorrect. Where is tan-¹x coming from?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Maclaurin Series

Hi Natkirky;

Your problem starts with log(x^2+1) ≠ arctan(x).

I understand what you were attempting to do. In numerical analysis we build one series from another. What you wanted was this:

From those you can build the Mclaurin series for log(x^2+1).

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If it ain't broke, fix it until it is.
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