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Homework Help: Help with a limit.

  1. Dec 18, 2011 #1
    1. The problem statement, all variables and given/known data

    question asks:

    lim(x,y) -> (0,0)

    cos(xy) -1 / [x^2 y^2]

    2. Relevant equations

    3. The attempt at a solution

    if you multiply the top and bottom by cos(xy) + 1 you get

    -[sin^2(xy)/(xy)^2] * [1/cos(xy) + 1]

    but in the solution they somehow got rid of the denominator (xy)^2, because if that's there the denominator is still 0. How do you get rid of that?
  2. jcsd
  3. Dec 18, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    The limit u->0 sin(u)/u=1. So limit u->0 sin(u)^2/u^2=1. That's what they did with the first term.
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