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Homework Help: Limit of serverable variables, need help

  1. Jun 13, 2008 #1
    1. The problem statement, all variables and given/known data
    (x,y)---> (0,0)
    x²+y²/√(x²+y²+1) - 1

    the -1 isnt in the square root, so people know




    3. The attempt at a solution
    i let y=o and got 2, and y=x² and x=y² and got 2, so how can i be sure this limit is 2, what other method must i try to be sure ?
     
    Last edited: Jun 13, 2008
  2. jcsd
  3. Jun 13, 2008 #2
    What exactly is the limit going to??? And your problem is very hard to interpret ... might want to re-type that with proper parenthesis.

    let x=y
     
    Last edited: Jun 13, 2008
  4. Jun 13, 2008 #3

    HallsofIvy

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    Science Advisor

    But is it in the denominator? Is this [itex](x^2+ y^2)/(\sqrt{x^2+ y^2})+ 1[/itex] or [itex](x^2+ y^2)/(\sqrt{x^2+ y^2}+ 1)[/itex] ?



    3. The attempt at a solution
    i let y=o and got 2, and y=x² and x=y² and got 2, so how can i be sure this limit is 2, what other method must i try to be sure ?[/QUOTE]
    One way to check is to change to polar coordinates. Since only r measures "distance to (0,0), if the limit, as r goes to 0, does not depend on [itex]\theta[/itex], that is the limit.
     
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