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Continuity of two variable function

  1. Jun 18, 2009 #1
    Hi Guy's I was wondering if anyone knows of a good link to explain the proof

    That if a function of two variables f(x,y) is differentiable at (x,y) than f(x,y) is continuous at (x,y)

    regards
    Brendan
     
  2. jcsd
  3. Jun 18, 2009 #2

    tiny-tim

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    Hi Brendan! :smile:

    (have a delta: δ and an epsilon: ε :wink:)
    That looks like a standard δ,ε proof …

    have a go, using the definitions of differentiable and continuous, and show us what you get. :smile:
     
  4. Jun 18, 2009 #3

    HallsofIvy

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    Crucial point: the definition of the derivative involves taking the limit of a fraction in which the denominator always goes to 0. What has to happen to the numerator?
     
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