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Math Help - Continuity & Limits

  1. #1
    Len
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    Continuity & Limits

    For what points is the function continuous?

    f(x,y)=\frac{xy}{x^2-y}

    Intuition tells me that it would be continuous everywhere except where the denominator equals zero so... Would it be continuous everywhere except on the parabola y=x^2?


    Also

    f(x,y)=\frac{x^4-4y^4}{x^2+2y^2}

    Find the limit of f(x,y) as (x,y)\rightarrow(0,0)

    Thanks for the help.
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  2. #2
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    For what points is the function continuous?

    f(x,y)=\frac{xy}{x^2-y}

    Intuition tells me that it would be continuous everywhere except where the denominator equals zero so... Would it be continuous everywhere except on the parabola y=x^2?
    Yes.

    f(x,y)=\frac{x^4-4y^4}{x^2+2y^2}

    Find the limit of f(x,y) as (x,y)\rightarrow(0,0)
    f(x, y) = \frac{(x^2 - 2y^2)(x^2 + 2y^2)}{(x^2 + 2y^2)}.

    Does this help?
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  3. #3
    Len
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    Quote Originally Posted by icemanfan View Post
    Yes.



    f(x, y) = \frac{(x^2 - 2y^2)(x^2 + 2y^2)}{(x^2 + 2y^2)}.

    Does this help?
    Saw that after I typed it up, but thought I better clarify :P, thanks a lot
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