anonymous
  • anonymous
what is the limit of 2x/x+3 as x approaches -3 from the left
Calculus1
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
graph it
anonymous
  • anonymous
I'd rather not be dependent on my calculator
Luigi0210
  • Luigi0210
Well then take a random, educated guess

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Luigi0210
  • Luigi0210
xD
Luigi0210
  • Luigi0210
And here come Psymon..
anonymous
  • anonymous
no really
Psymon
  • Psymon
Well, because there is no way to eliminate that x+3 denominator, this means that there must be an asymptote at x = -3. If there was not an asymptote, thered be a way to eliminate the x+3 denominator to make the limit exist. SO that being said, we know this graph will go to infinity or negative infinity at x = -3. So we just need to check a couple values of x as it approaches -3 from the left. So from the left of -3 means -6, -5, -4, etc. So if we test -4: \[\frac{ 2(-4) }{ -4+3 }= 8\]So now we will test -3.5, even closer to -3 and see if our function value decreased or increase. Plugging in -3.5 I get: \[\frac{ 2(-3.5) }{ -3.5+3 }= 14 \]Well, our function value shot up. So for sure that as we approach -3 from the left, we will go to positive infinity.
Luigi0210
  • Luigi0210
^
anonymous
  • anonymous
So you could say there isn't a limit?
Psymon
  • Psymon
It kind of depends on what section of the text you are in. Earlier on in an intro to limits, you would say does not exist. But once you get introduce to limits to infinity, you would say the limit is positive infinity. It all depends on where you actually are in your calculus course.
Luigi0210
  • Luigi0210
If you're in calc there is a limit, if you're in pre-calc you must likely take DNE as an answer
Luigi0210
  • Luigi0210
*most
anonymous
  • anonymous
We were just introduced to limits on thursday, so for now im going to put does not exist. thanks slugger
Psymon
  • Psymon
Sure ^_^
Luigi0210
  • Luigi0210
._.
Psymon
  • Psymon
Cheer up @Luigi0210 ^_^

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