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 $\displaystyle f(x) = 2x^3 - 3x^2 + 4x - 5$

(a) at $\displaystyle x = 0$ (b) at $\displaystyle x = 1$

(a) is already centered at $\displaystyle x = 0$.

(b) I did Taylor series and got this: $\displaystyle P_{3}(x) = 2(x-1)^3 + 3(x-1)^2 + 4(x-1) - 2$

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.