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Math Help - Continuity

  1. #1
    Newbie
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    Continuity

    Hi,
    Can anybody help me out with this.........



    If f(x) = x , if x is a integer
    10 -x , if x is a real number which is not an


    Find whether f is continuous at x = 5.


    Thanks
    Arun.
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    Quote Originally Posted by arunkayal View Post
    Hi,
    Can anybody help me out with this.........



    If f(x) = x , if x is a integer
    10 -x , if x is a real number which is not an


    Find whether f is continuous at x = 5.


    Thanks
    Arun.
    Yes, f is continuos at x=5.

    I don't know now, or I forgot the rules, about proving continuity. Just by reasoning/analyzing, I believe f is continuous at x = 5.

    When x is not an integer, f(x) tends to be 5 coming from the left or coming from the right. At x=5, the second piece of the f is a hole because x=5 is not in the domain of that piece, for 5 is an integer.

    But the first piece takes over. The hole at x=5 is filled up by the f(x) = x of the first piece. Hence x=5 is true for the piecewise f function.
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