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Analyze the continuity

  1. Jul 31, 2011 #1
    How would I analyze the continuity of:

    g(x,y) = sin(2x^2 - y^2) / 2x^2-y^2 unless y^2=2x^2
    1 if y^2=2x^2

    g(x,y) seems to be continuous for all values of (x,y)... However, I realize that the function assumes the value 0 when y^2=2x^2. I am not really sure how to go further than this... the function seems to be continuous, unless we specify that it assumes 1 when y^2=2x^2, which makes the function discontinuous.

    Am I missing something?
     
    Last edited: Jul 31, 2011
  2. jcsd
  3. Jul 31, 2011 #2

    Dick

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    Re: Continuity

    The function doesn't assume the value 0 if y^2=2x^2, the ratio sin(2x^2 - y^2) / 2x^2-y^2 undefined if y^2=2x^2 because it has a zero denominator. What's the limit of sin(2x^2 - y^2) / 2x^2-y^2 as 2x^2-y^2 approaches zero?
     
    Last edited: Jul 31, 2011
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