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Math Help - A two variable limit

  1. #1
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    A two variable limit

    The following limit exists, but I can't find its value: \displaystyle\lim_{(x,y)\to(0,2)}\frac{(y-2)^2\sin(xy)}{x^2+y^2-4y+4}.

    Hope you can help me.
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  2. #2
    Forum Admin topsquark's Avatar
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    If the limit exists (and I haven't gone so far as to prove that) then it must exist for x, y --> (0, 2) from any way of approaching the point (0, 2). What I would do is to take, say, y = x + 2. Then after you sub y = x + 2 into the limit, you evaluate it for x --> 0.

    -Dan
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  3. #3
    Super Member General's Avatar
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    \left| \dfrac{(y-2)^2 sin(xy)}{x^2+y^2-4y+4} \right| \leq sin(xy)

    Use sandwich.
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