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Math Help - find limit

  1. #1
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    find limit

    f(x,y)= (xy)/x^2+y^2

    prove there is no value for f is continuous at (0,0).
    they say I can use x=y => it will have 2 limit

    but I don't know how to do it.

    PlX Help...
    Last edited by mathbeginner; November 6th 2010 at 03:03 PM.
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  2. #2
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    What is the limit at (0,0):
    i) along the x\text{-axis}?
    ii) along the line y=x?
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  3. #3
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    Quote Originally Posted by Plato View Post
    What is the limit at (0,0):
    i) along the x\text{-axis}?
    ii) along the line y=x?

    what do u mean along the x-axis
    is it x=o?
    then the function will become 1/y but the
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  4. #4
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    Quote Originally Posted by mathbeginner View Post
    what do u mean along the x-axis
    is it x=o?
    then the function will become 1/y but the
    It helps to finish asking the question ....

    You should have been taught how to tale limits along different paths. Along the x-axis, y = 0. Taking the limit x --> 0 your function clearly approaches 0.

    Along the line y = x, you need to consider \displaystyle \lim_{x \to 0} \frac{x^2}{x^2 + x^2}.

    Are these two limits the same? Draw a conclusion.
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  5. #5
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    Along the line y=x you have \dfrac{x^2}{x^2+x^2}.
    So what is the limit?
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  6. #6
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    thx a lot...
    I think I make a careless mistake.
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