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Math Help - definiton of differentiated and continuous

  1. #1
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    definiton of differentiable and continuous functions

    All the definitions i know refers to situation where I can tell if funcion f is continuous or diferentiable in particular point a. But now i got an assignment, where i must tell if function is continuous and diferentible in general?
    Can anybody help? Because I can't find the answere anywhere.
    And I think that definition, like, f is diferentiable(continuos) in domain (a;b) if it is diferentiable in all the particular points, doesn't work for me, because it is not possible to check all the points.
    Last edited by waytogo; October 12th 2010 at 03:26 AM.
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  2. #2
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    Quote Originally Posted by waytogo View Post
    But now i got an assignment, where i must tell if function is continuous and diferentible in general?
    Can anybody help? Because I can't find the answere anywhere.
    And I think that definition, like, f is diferentiable(continuos) in range (a;b) if it is diferentiable in all the particular points, doesn't work for me, because it is not possible to check all the points.
    Well, I am sorry that does not work for you because it is in fact the answer. There is one change. The word range should be domain.
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  3. #3
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    Quote Originally Posted by Plato View Post
    There is one change. The word range should be domain.
    I'm sorry, that's because of my English. I have corrected it now.

    Well, but maybe it is possible to use any theorem, which then allows to include the function in a class of functions, which are known to be differentiable? Because otherwise this task seems incomplete for me. But it shouldn't be, because I checked it with my lecturer.
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  4. #4
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    You don't actually check individual points, you check if the function is differentiable at some "general" x. But there simply is no simpler description of "differentiable on set X" than "differentiable at every point of x".

    Now, what "task" are you talking about? Exactly what is your question?
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  5. #5
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    task:
    f(x,y)=\sqrt[3]{sin(x^3+y^3)}
    1) Is f diferentiable?
    2) Is f_x,f_y ( f_x=\frac{\partial f}{\partial x} , f_y=\frac{\partial f}{\partial y}) continuous?
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