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Math Help - find limit f(X) as x approaches __

  1. #1
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    find limit f(X) as x approaches __

    f(x) = x^3 +3 x< -1
    x^2 +x +1 -1<x<1
    x^4 +2 x> 1


    1) for the function whose graph is given above, the limit f(x) as x approaches -1+ is:

    x^2+x+1 touch -1 from right side first so I plug in -1 and get 1

    2) The limit f(x) as x approaches -1 is


    since only x^3+3 and x^2+x+1 touches -1, I plugin -1 in both equation.

    x^3+3 = 2
    x^2+x+1 = 1

    the limit does not exists.


    can this method be applied to all problems similar to this one?
    this is all assuming I don't have a graphic utility, don't know how to graph by hand, don't know of polynomial are contentious




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  2. #2
    Super Member TheChaz's Avatar
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    Re: find limit f(X) as x approaches __

    You have used the "direct substitution" method of limit evaluations. It works in this case, but not always.
    Consider
    g(x) = \frac{x^2 - 4}{x + 2}

    And take the limit as x approaches -2. You'll find that you get 0/0, an indeterminate form.
    In this example, you would factor to get "x - 2" (when x is not equal to 2) and then directly substitute.

    But so far, you haven't done anything wrong!
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