Infinite (power) series question

[Scrapster]

We just went over this in class the other day and derived the formula:


Fn(x) = Sum (f^(b)*(a))/(k!))*(x-a)^(k)
^
factorial

This is a practice problem I'm trying to work out, but not getting anywhere.
f(x) = sin(x)

I think I'm just not understanding the use of all the different variables. I think (b) is the # of derivative, k is the exponent, x is your point. And I think "a" is supposed to equal zero.

Anyone familiar with Taylor series? I could use some pointers.

 

[AlphaIVT]

Confucisous says: "If Scrapster isn't familiar with Taylor series, he gets no where"

 

[Scrapster]

Scrapster agrees.

 

[AlphaIVT]

Confuscious says: "If Scrapster stops saying "Confuscious says:..." , he will learn Taylor series."

 

[arod324]

The "a" in this equation is in reference to the to the point. In a McClaurin series, this equals zero, therefore it is only x^1 or X^2 whereas in a taylor series it'll be something along the lines of (x-4)^1 or (x-4)^4 where 4 is (i believe) the distance from the "real" point that you trying to estimate.... let me look at my book and i'll help you some more

 

[arod324]

In my book the equation = " f(c) +f`(c)(x-c) + ................. (F^(n)(c)*(x-c)^n)/n!.......... this is the taylor series for F(x) at c.... and the mcclaurin is when "c" equals zero..

 

[arod324]

BTW, what does the problem say that "c" is, or is it a mcclaurin where the "c" equals zero.... so i can help you out... it's actually been about 3 months since I've done these... but I still can remember some of it.. (with a book )

 

[Pyro]

Pyro says: "Pyro does not like people who refer to themselves in thrid person"