Help with representations of functions as power series please

Question

anonymous · Answer

f(x) = 5x^3 -13x^2 + 7

perl · Answer

where is it centered at

anonymous · Answer

It doesn't say. I'm not sure what that even means

perl · Answer

a power series is an expression of the form 
Sum a*(x-c)^n

alekos · Answer

I'd say assume that it's centred at 0,  so c=0

alekos · Answer

That'll make it a McLaurin Power Series

$$f(x) = \sum_{0}^{\inf?}f^{n}(0)x ^{n}/n!$$

alekos · Answer

I'll leave the rest to you

perl · Answer

as a 'power series' it is basically already given in the right form

anonymous · Answer

I don't think it's meant to be solved as a McLaurin Power Series as that is the next section in my book that my class didn't cover yet.

perl · Answer

http://en.wikipedia.org/wiki/Power_series

alekos · Answer

so what are they asking you to do?

perl · Answer

f(x) = 5x^3 -13x^2 + 7
As a power series we can write this centered at c = 0 as :
 7 + 0*(x-0) + (-13)*(x-0)^2 + 5*(x-0)^3 + 0 *(x-0)^4 + ... 

the rest of the coefficients will be zero

perl · Answer

just to put in the form 
Sum a * (x-c)^n , n=0 .. infinity

anonymous · Answer

So am I supposed to find a pattern?

perl · Answer

no, there is no pattern. i think its just saying you can write any polynomial as a power series

perl · Answer

a polynomial is a member of the class of functions that can be represented by power series

anonymous · Answer

Ohhh it just wants it in the expanded form???? I was dying from trying to find the summation form

alekos · Answer

it's kind off a trick question

anonymous · Answer

Ya I see now. Thanks

perl · Answer

read this part http://en.wikipedia.org/wiki/Power_series#Examples

perl · Answer

to center it at another value takes a bit more work. 
but you can center a polynomial at any value :)

anonymous · Answer

Makes sense :)