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Homework Help: Explain why this function is discontinuous

  1. Mar 10, 2008 #1
    1. The problem statement, all variables and given/known data
    Using the test for continuity at a point, explain why each function is discontinuous at the given x-value. Classify each discontinuity.

    the question is a piecewise function.

    i(x)={(x^2+5x+4)/(x^3+1), x=/= -1
    {2, x=-1

    this is all one piece wise function.

    3. The attempt at a solution

    I first can say that the function exists and the limit exists just by glance. At x=-1 for the first piece, it is indeterminent. So I factor the first piece and end up with:

    lim (x+4)/(x^2+x+1)

    subbing in a negative one I get 3.

    but the back of the book says:

    lim i(x) =2

    I'm not sure how.
  2. jcsd
  3. Mar 10, 2008 #2


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    you should get x^2-x+1 and not x^2+x+1. But I get 1 instead of 2 still...
  4. Mar 10, 2008 #3
    nvm, the book must be wrong..
  5. Mar 10, 2008 #4


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    Well, for one thing you factored the denominator wrong. Are you sure the back of the book doesn't say lim(i(x))=1 as x->-1?
  6. Mar 11, 2008 #5
    I think the book's wrong seeing as it wants you to show why the function is not continuous, when its answer would actually show that it is continuous at x=1... I think rock freak is right on this one.
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