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Math Help - Continuous function

  1. #1
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    Continuous function

    Hey.
    How can I show that this is a Continuous function?
    Attached Thumbnails Attached Thumbnails Continuous function-1.jpg  
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  2. #2
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    You need to show that f(0,0)=\underset{(x,y)\to (0,0)}{\mathop{\lim }}\,=\frac{x^{2}y^{2}}{x^{2}y^{2}+(x-y)^{2}}=1.
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    You need to show that f(0,0)=\underset{(x,y)\to (0,0)}{\mathop{\lim }}\,=\frac{x^{2}y^{2}}{x^{2}y^{2}+(x-y)^{2}}=1.

    Yeah, I know that.
    I don't have a clue how to show that, any idea?
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  4. #4
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    Quote Originally Posted by asi123 View Post
    Yeah, I know that.
    I don't have a clue how to show that, any idea?
    It is not true.
    Different paths give different answers.
    The path x=y gives the limit 1.
    While the path x=0 gives the limit 0.
    Thus, the limit does not exist.
    Thus, the function is not continous.
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