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RE: [apcalculus] limit from Stu Schwartz
Posted:
Oct 22, 2012 8:51 PM


NOTE: This apcalculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/gettingstarted and post messages there.  For any polynomial the "end behavior" of the polynomial mirrors that of the leading term. In your example the polynomial behaves like 3x^4 and this goes off to +oo as x>+oo or as x>oo.
I give my kids a heuristic argument (a fancy term for hand waving) that goes like this: When x is a trillion, x^4 is a trillion times bigger than x^3.......and then fast talking and hand waving but the gist is there.
Another argument says lim(x>+/oo)p(x)/(3x^4)=1 where p(x) is your polynomial. If the ratio is getting close to 1 and the denominator is going to oo than p(x) must also be going to oo.
HTH
Doug  Doug Kühlmann Math Dept Phillips Academy Andover, MA 01810
________________________________________ From: Tammy Slack [tslack@bgcsd.org] Sent: Monday, October 22, 2012 9:16 AM To: AP Calculus Subject: [apcalculus] limit from Stu Schwartz
NOTE: This apcalculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/gettingstarted and post messages there.  Can anyone tell me how to solve the limit as x approaches negative infinity of (3x^4  3x^3 + 5x^2 + 8x  3)? I assume it is positive or negative infinity but don't know how to tell which it is.  To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apcalculus
 To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apcalculus



