# help with the taylor series for a bonus problem

• May 29th 2007, 09:38 PM
thatguyinthesuit
help with the taylor series for a bonus problem
hey all,

i am stuck on a math problem that no one i've talked to can figure out. the idea is i have to find a taylor series in x - a through the term (x - a)^3 for the problem:

2 - x + 3(x^2) - x^3 , a = -1

if anyone has ANY idea at all how this is done, please let me know. thank you.
• May 29th 2007, 11:17 PM
CaptainBlack
Quote:

Originally Posted by thatguyinthesuit
hey all,

i am stuck on a math problem that no one i've talked to can figure out. the idea is i have to find a taylor series in x - a through the term (x - a)^3 for the problem:

2 - x + 3(x^2) - x^3 , a = -1

if anyone has ANY idea at all how this is done, please let me know. thank you.

put \$\displaystyle u=x-a\$, then \$\displaystyle x=u+a\$ now substutute this into your expression to get:

\$\displaystyle
2 + (u+a) + 3(u+a)^2 -(u+a)^3
\$

now expand the powers and collect terms to give a cubic in \$\displaystyle u\$ and finaly replace \$\displaystyle u\$ by \$\displaystyle x-a\$

RonL