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Another math limit problem

  1. Feb 5, 2009 #1
    1. The problem statement, all variables and given/known data
    lim
    x[tex]\rightarrow[/tex]2 ((1/x)-(1/2))/(x-2)


    2. Relevant equations



    3. The attempt at a solution
    Limit x-> for all of them, too tedious to keep rewriting it
    =((2/2x)-(x-2x))/(x-2)
    =((2-x)/(2x))/(x-2)
    =((2-x)/(2x)) * (1/(x-2))
    =(2-x)/(2x^2-4x)
    sub 2 in = 0/0 = 0

    therefore when x approaches 2, y approaches 0?

    =
     
  2. jcsd
  3. Feb 5, 2009 #2

    Dick

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    Re: Limits

    Never say 0/0=0. Never, until you have actually shown it. You have (2-x)/((2x)*(x-2)). (2-x)/(x-2)=-(x-2)/(x-2)=(-1). Now what's the limit?
     
  4. Feb 5, 2009 #3
    Re: Limits


    How did you go from (2-x)/((2x)*(x-2)) to (2-x)/(x-2)?
     
  5. Feb 5, 2009 #4

    Dick

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    Re: Limits

    I didn't. I just separated (2-x)/((2x)*(x-2)) into [1/(2x)] * [(2-x)/(x-2)] and made the observation that the second factor is -1.
     
  6. Feb 5, 2009 #5
    Re: Limits

    So then it is 0?

    Btw, does the derivative of x/(2x-1) = 0?
     
  7. Feb 5, 2009 #6

    Dick

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    Re: Limits

    Is what 0? No, the derivative of x/(2x-1) is not zero. Unless x=0.
     
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