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Math Help - interpreting graphs of limits...

  1. #1
    Junior Member
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    interpreting graphs of limits...

    ok so say you have

    the lim as x approaches -1 from the right f(x) = f(-3)

    Apparently it's true by looking at the graph. The point at f(-3) =1.
    And as lim as x approaches -1 from the right, it is an open circle which is 1 and a closed circle which is 2.

    -I don't know why that is true since f(x) = 2 points where one is and open point and one is a closed point...I thought if you had an open and closed point then that would mean it isn't continuous or differentiable or something?
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  2. #2
    MHF Contributor
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    The right hand limit and left hand limits can be different and are different for the graph you've described. It doesn't matter what the value is at the point for one-sided limits, only the point that the graph is approaching. You are right, at x=-3 this graph isn't differentiable because true limit doesn't exist for this point.
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