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Math Help - Limits in two Dimensions

  1. #1
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    Limits in two Dimensions

    How can I calculate the following limits or prove that don't exist:

    a) \lim_{(x,y) \to (0,0)} \frac {x^4 + y^4}{x^2 + y^2}

    b) \lim_{(x,y) \to (0,0)} \frac {x^2 - y^2}{x^2 + y^2}

    Thanks in advance
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  2. #2
    MHF Contributor
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    Quote Originally Posted by ypatia View Post
    How can I calculate the following limits or prove that don't exist:

    a) \lim_{(x,y) \to (0,0)} \frac {x^4 + y^4}{x^2 + y^2}

    b) \lim_{(x,y) \to (0,0)} \frac {x^2 - y^2}{x^2 + y^2}

    Thanks in advance
    Hi

    a) \frac {x^4 + y^4}{x^2 + y^2} \leq x^2+y^2

    b) On the x axis \frac {x^2 - y^2}{x^2 + y^2} = 1 but on the y axis \frac {x^2 - y^2}{x^2 + y^2} = -1
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