Hi everyone. I am a senior in high school taking AP Calc BC and I have a question on Power Series. I just finished taking notes on Section 9.1 (Power Series) and 9.2 (Taylor Series) in this textbook: Amazon.com: Calculus: Graphical Numerical Algebraic (9780130631312): Ross L. Finney, Franklin Demana, Bert K. Waits, Daniel Kennedy: Books - Anyhow, my question is, why move a function's center? For example:
Find the third order Taylor polynomial for
(a) at (b) at
(a) is already centered at .
(b) I did Taylor series and got this:
I graphed out the two equations and they are exactly identical. So what is the point of moving the center? Not Answered
Another question: is there a thread on using the [tex] tag? Answered
Any help is appreciated. Thanks in advance.
Understand that Taylor polynomials are used as approximations for non-polynomial functions.
A Taylor polynomial for a polynomial function is just that particular polynomial, no matter where it is centered, i.e nothing is gained by its representation.
Try determining a Taylor polynomial for a non-polynomial function ... you'll se that the centering point will be the only point where the Taylor polynomial = the function of interest.