65F. Terminal behaviour - JulTob/Mathematics GitHub Wiki
We may be interested, for many reasons, as to how a function behaves on an unlimited increase or decrease of $x$ as it goes away from $0$
-
$xâ¶â$
Means " $x$ grows in the positive direction of â". -
$xâ¶ïżąâ$
Means " $x$ grows in the negative direction of â".
Example: Even Polynomials
- When $xâ¶â$ then $đ_{2n}[x]â¶â$
- When $xâ¶ïżąâ$ then $đ_{2n}[x]â¶â$
Example: Odd Polynomials
- When $xâ¶â$ then $đ_{2n-1}[x]â¶â$
- When $xâ¶ïżąâ$ then $đ_{2n-1}[x]â¶ïżąâ$
Then: The behavior of any polynomial $đ_{n}[x]$ corresponds to the highest non-zero term.