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Limit Problem

  1. Feb 24, 2016 #1
    1. The problem statement, all variables and given/known data
    Find the following limits, if they exist.

    2. Relevant equations


    3. The attempt at a solution
    I have just started calculus and am having trouble with 3 a). I get 0/0 after substitution so I factored but still get 0 in the denominator. Does this indicate that the limit does not exist? Am I doing the questions correctly? My work is attached below. Thanks! All help is very much appreciated.
    View attachment 96417 https://www.physicsforums.com/attachments/96417/
     
    Last edited by a moderator: Feb 25, 2016
  2. jcsd
  3. Feb 24, 2016 #2
    You're taking the limit of a constant (3) divided by something which approaches zero. What do you get if you divide a positive constant by an infinitesimal quantity?
     
  4. Feb 24, 2016 #3
    Undefined = DNE?
     
  5. Feb 24, 2016 #4
    Or would it be positive infinity?
     
  6. Feb 24, 2016 #5

    vela

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    You could also consider the graph of ##\frac{x+2}{x-1}##. It should be clear from that that the limit doesn't exist.
     
  7. Feb 24, 2016 #6
    Yes, but you can approach 1 from both sides. ##lim_{x\rightarrow 1^+} \frac{x+2}{x-1}## must be equal to ##lim_{x\rightarrow 1^-} \frac{x+2}{x-1}## for the limit to exist. Are they?
     
  8. Feb 25, 2016 #7

    HallsofIvy

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    Saying that a limit "is positive infinity" is just saying that "the limit does not exist" but giving a specific reason- that the values get larger and larger and larger without upper bound, as opposed to getting lower and lower without lower bound or jumping around without getting close to any one specific number.
     
  9. Feb 25, 2016 #8

    Ray Vickson

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    Very nice explanation.
     
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