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Math Help - Limits by definition - 2 variables function

  1. #1
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    Limits by definition - 2 variables function

    Could anyone please help me proving by definition that:

    lim_(x,y)-->(2,1) f(x,y)=3

    where f(x,y)= (x+y) / (x-y)

    Thank you in advance.
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  2. #2
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    Quote Originally Posted by johnnashfcup View Post
    Could anyone please help me proving by definition that:

    lim_(x,y)-->(2,1) f(x,y)=3

    where f(x,y)= (x+y) / (x-y)

    Thank you in advance.
    The numerator and denominator are both continuous functions, so the only place where f(x, y) is not continuous is where the denominator  = 0. This does not occur at (x, y) = (2, 1), so you can just use direct substitution.


    \lim_{(x, y) \to (2, 1)}\frac{x + y}{x - y} = \frac{2 + 1}{2 - 1}

     = \frac{3}{1}

     = 3.
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  3. #3
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    Thanks for the answer but I would like a prove using the limit definition...
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