help with maclaurin/taylor series

page89

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Nov 20, 2007
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Hi guys,

I have recently been taught about the maclauren/taylor series and i have been set the following questions but i am struggling with them and i was hoping someone could help,

Q. Determine the Maclaurin series upto the term in x^3 for each of the following functions (you may assume Maclaurin series for standard functions)

part i) (1 + x) ^ (2/3)

part ii) x / (1 + 3x) ^ 3

part iii) (1 + x^2) sin x


I would be really gratefull if anyone can help me with them they have to be done for tomorrow
 
x(1+3x)3\displaystyle \frac{x}{(1+3x)^{3}}

k=03fk(0)k!=f(0)+f(0)x+f(0)2!x2+f(0)3!x3\displaystyle \sum_{k=0}^{3}\frac{f^{k}(0)}{k!}=f(0)+f'(0)x+\frac{f''(0)}{2!}x^{2}+\frac{f'''(0)}{3!}x^{3}

f(0)=0\displaystyle f(0)=0

f(0)=1\displaystyle f'(0)=1

f(0)=18\displaystyle f''(0)=-18

f(0)=324\displaystyle f'''(0)=324

Assemble it:

x9x2+54x3\displaystyle x-9x^{2}+54x^{3}
 
Thanks I knew it had something to do with differentiating each term but i think i went wrong trying fo differentiate it for the 3rd time.

Thanks.

Can anyone help with the others?
 
page89 said:
Thanks I knew it had something to do with differentiating each term but i think i went wrong trying fo differentiate it for the 3rd time.

Thanks.

Can anyone help with the others?

Please show us your work - and exactly where you are stuck - so that we would know where to begin.
 
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