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Homework Help: Limit of a function

  1. Jan 21, 2012 #1
    1. The problem statement, all variables and given/known data
    http://www4b.wolframalpha.com/Calculate/MSP/MSP10351a01a355263db6f2000030459ebe888feb73?MSPStoreType=image/gif&s=10&w=131&h=41 [Broken]
    I know the answer, but I don't know how to get it.

    2. Relevant equations
    If picture doesn't work: limit x->1 (x-1)/((square root(x+3) - 2)


    3. The attempt at a solution
    I know that when you plug in 1, the answer becomes 0/0, which means I need to factor. I don't know how to factor this equation, though.
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Jan 21, 2012 #2
    http://www.mathway.com/math_image.aspx?p=SMB02LSMB03x:1,SMB02FSMB03x-1SMB10SMB02RSMB03x+3SMB02rSMB03-2SMB02fSMB03SMB02lSMB03?p=93?p=46 [Broken]

    If this is the equation, the limit does not exist, the answer should be DNE! The way you do it is basically plug in 1 and then you will get 0 on the top and basically it won't exist.
     
    Last edited by a moderator: May 5, 2017
  4. Jan 21, 2012 #3
    This function definitely HAS a limit as x approaches 1. Just because it evaluates as 0/0 does not necessarily mean the limit does not exist. Instead, you can use other methods like multiplying by a conjugate, factoring, L'Hôpital's Rule, etc.

    with that being said, you could use L'Hôpital's Rule, but I'd recommend multiplying by the conjugate as sheriff89 said.
     
    Last edited by a moderator: May 5, 2017
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