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Math Help - Determining Points of a Func. That are Continuous

  1. #1
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    Determining Points of a Func. That are Continuous

    Given the functions below, determine all the points where the function given is continuous.

    1.) f(x,y,z) = (x^3)/(y) + sin(z)

    2.) Note: this function is a piecewise function:

    Code:
    f(x,y) = cos(1/(x^2 + y^2)), if (x,y) =! (0,0)
                 1,              if (x,y) = (0,0)
    Also note that =! means "does not equal"

    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by Ideasman View Post
    Given the functions below, determine all the points where the function given is continuous.

    1.) f(x,y,z) = (x^3)/(y) + sin(z)
    This is some combination of those standard (elementary) functions. Thus, the "bad" points are the undefined points.
    In this case it is y=0.

    Thus,
    S={(x,y,z)| such that y ! = 0}
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