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Greatest integer function limit problem. Proving whether the limit exists

  1. Nov 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that the limit exists.
    lim 5 - 1/2[[2x]]
    x-->1
    Show your solution..
    2. Relevant equations



    3. The attempt at a solution
    Tried getting the limit from the right and left.. not sure if what I've done is right though but this is what I got.

    lim 5 - 1/2[[2x]] ===> 5-1/2(2(1)) ====> 4
    x-->1+

    lim 5 - 1/2[[2x]] ===> 5-1/2(2(1)) ====> 4
    x-->1-

    The answer I got is equal in both ways, therefore the limit exists.

    If I'm wrong tell me where and help me please.
     
  2. jcsd
  3. Nov 14, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    It would help if you told us what [[x]] meant! I thought it might be the "floor function" but if that were true then for 0< x< 1, [[2x]] would be 0, not 2, so the lower limit would be 5, not 4.
     
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