# FP2 Maclaurin series question

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#1
Hi!

The question is by expanding (1-4x^2)-(1/2) and integrating term by term, find the series expansion for arcsin(2x) as far as the term x^7.

I know how to do normal Maclaurin expansion but I keep getting stuck here. Each time I differentiate, I just end up with all of the f'(0)= 0 which means there isn't a proper expansion.

Any help??
0
3 years ago
#2
(Original post by munchkin1212)
Hi!

The question is by expanding (1-4x^2)-(1/2) and integrating term by term, find the series expansion for arcsin(2x) as far as the term x^7.

I know how to do normal Maclaurin expansion but I keep getting stuck here. Each time I differentiate, I just end up with all of the f'(0)= 0 which means there isn't a proper expansion.

Any help??
So you have , what is your expansion? You're told to integrate each term, not differentiate them. Also, might help to write down the derivative of
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#3
(Original post by RDKGames)
So you have , what is your expansion? You're told to integrate each term, not differentiate them.
I don't know how to expand it - Binomial expansion?
0
3 years ago
#4
(Original post by munchkin1212)
I don't know how to expand it - Binomial expansion?
Yes

EDIT: If you MUST use MacLaurin's and you've failed to apply it, post your working because it should work.
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#5
(Original post by RDKGames)
Yes

EDIT: If you MUST use MacLaurin's and you've failed to apply it, post your working because it should work.
It's much simpler now I've used Binomial, thanks.
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#6
(Original post by RDKGames)
Yes

EDIT: If you MUST use MacLaurin's and you've failed to apply it, post your working because it should work.
In another question, it says:

By integrating 1/(1+x^2) and its Maclaurin expansion, find the Maclaurin series for arctanx.

I'm struggling to find the Maclaurin series for (1+x^2)^-1

Each time I differentiate I just get f'(0) and f''(0) to equal 0. Where am I going wrong?
0
3 years ago
#7
(Original post by munchkin1212)
In another question, it says:

By integrating 1/(1+x^2) and its Maclaurin expansion, find the Maclaurin series for arctanx.

I'm struggling to find the Maclaurin series for (1+x^2)^-1

Each time I differentiate I just get f'(0) and f''(0) to equal 0. Where am I going wrong?
You're probably doing the same mistake as before.

and clearly
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#8
(Original post by RDKGames)
You're probably doing the same mistake as before.

and clearly
Eugh I completely forgot I had to use the product rule! Sorry to have bothered you with my silly mistakes - thanks again!
0
3 years ago
#9
(Original post by munchkin1212)
Eugh I completely forgot I had to use the product rule! Sorry to have bothered you with my silly mistakes - thanks again!
By the way, this is yet another problem where you shouldn't be differentiating over and over again. Instead, you should realise that is a geometric series so

This is only valid for though, but using you can recover a series for |x| > 1 although I suspect you don't need that in this question.
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