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Math Help - Function in two variables - continuity

  1. #1
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    Function in two variables - continuity

    Hello,
    Still struggling with these proofs, some help would be appreciated
    Can the function
    f(x,y) = \frac {\sin x\sin^3 y}{1 - \cos(x^2+y^2)}
    be defined at (0,0) in such a way that it becomes continuous there? Prove your answer.

    Regards,
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  2. #2
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    Quote Originally Posted by Robb View Post
    Hello,
    Still struggling with these proofs, some help would be appreciated
    Can the function
    f(x,y) = \frac {\sin x\sin^3 y}{1 - \cos(x^2+y^2)}
    be defined at (0,0) in such a way that it becomes continuous there? Prove your answer.

    Regards,
    no it can't! because \lim_{(x,y)\to(0,0)} f(x,y) doesn't exist: \lim_{x\to0}f(x,x)=\frac{1}{2} but \lim_{x\to0}f(x,-x)=\frac{-1}{2}.
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