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Math Help - Continuous extension at a point

  1. #1
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    Continuous extension at a point

    I have the function
    f(x) = (x^8)\ |x-2|

    I have to determine if the function has a continuous extension at x=2 ???

    My solution is

    1- Lim (x-2)(x^2+2x+4)\(x-2)= 12 if x>or equal to 2
    x goes to 2

    2- Lim (x-2)(x^2+2x+4)\ - (x-2)= -12 if x less than 2
    x goes to 2


    Is there a continuous extension at x=2 ??????????????? although we have two values (12, -12) because of (absolute value) ??

    or there is not continuous extension ??






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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by mariama View Post
    I have the function
    f(x) = (x^8)\ |x-2|

    Of course you meant f(x)=(x^3-8)/(|x-2|) .

    You have correctly found the left and right hand limits, and they are distinct so, does dot exist the limit as x\to 2 . Hence, f has not a continuous extension at x=2 .


    Fernando Revilla
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