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Math Help - Help on continuity

  1. #1
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    Help on continuity

    Determine the number at which the function is discontinuous, and show why definition 1.8.1 isnt satisfied at this number
    Def 1.8.1
    1.) f(a) exists
    2.) \lim_{x \to a} exists
    3.) \lim_{x \to a} = f(a)

    12.)H(x) =
    6 + xif x \leq -2
    2 - xif   -2 < x \leq 2
    2x - 1if 2 < x

    sorry and thanks very much for your help
    Last edited by ^_^Engineer_Adam^_^; December 16th 2006 at 04:07 AM. Reason: I Accidentally pressed enter
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  2. #2
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post

    12.)H(x) =
    6 + xif x \leq -2
    2 - xif   -2 < x \leq 2
    2x - 1if 2 < x
    The only possible points are x=-2,2
    Check x=-2.

    \lim_{x\to -2}H(x) what is it?
    When we approach from the right and from the left we have respectively,
    6+(-2)=4
    2-(-2)=4.
    Continous!

    \lim_{x\to 2}H(x) what is it?
    When we appraoch from the right and from the left we have respectively,
    2-(2)=0
    2(2)-1=3
    Thus it is discontinous.
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