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Topic: [ap-calculus] limit from Stu Schwartz
Replies: 1   Last Post: Oct 22, 2012 8:51 PM

 Doug Kuhlmann Posts: 3,630 Registered: 12/6/04
RE: [ap-calculus] limit from Stu Schwartz
Posted: Oct 22, 2012 8:51 PM

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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
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Doug Kühlmann
Math Dept
Andover, MA 01810

________________________________________
From: Tammy Slack [tslack@bgcsd.org]
Sent: Monday, October 22, 2012 9:16 AM
To: AP Calculus
Subject: [ap-calculus] limit from Stu Schwartz

NOTE:
This ap-calculus 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/getting-started
and post messages there.
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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.
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