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Math Help - Continuity question

  1. #1
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    Continuity question

    Hi

    Analyse the continuity of the function
    z = (xy-5)/(x^2+y^2-4)

    I checked that z approaches infinity when x^2+y^2=4 so, this circle represents the discontinuity points. Is this right?

    Thanks
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  2. #2
    MHF Contributor

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    Yes, that is correct. This function is continuous everywhere except on the circle x^2+ y^2= 4.
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  3. #3
    MHF Contributor
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    You need to check that there are no points on the circle where xy = 5
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