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Math Help - 3 Questions (Limits)

  1. #1
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    3 Questions (Limits)

    Here are three questions which I'm trying to solve. The first one I solved but was hoping someone could verify because I'm not sure that the solution is right. The 3rd one I need help on because I can't factor out or cancel anything.



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  2. #2
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    The first 1 you can substitute.

    The third one you get (SOMETHING)/0 where SOMETHING
    not = zero. Thus it is + infinity.

    The second one you get 0/0 which is bad.
    You factor,

    x^3-3x^2+4
    x^3-2x^2+4-x^2
    x^2(x-2)+(2-x)(2+x)
    x^2(x-2)-(x-2)(x+2)
    (x-2)(x^2-x-2)

    Now you can cancel (x-2) to get,

    x^2-x-2 and take limit as x -- > 0
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  3. #3
    Junior Member frenzy's Avatar
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    for #3 the limit does not exist. ( it is not +\infty)
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  4. #4
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    So you can substitute in the first one and say that it approaches 0 when you substitute it gives 0/3 which equals 0?

    And I still don't understand the 3rd one. Is there a way to actually show if it's approaching + or - infinity?
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  5. #5
    Junior Member frenzy's Avatar
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    Quote Originally Posted by SportfreundeKeaneKent View Post
    So you can substitute in the first one and say that it approaches 0 when you substitute it gives 0/3 which equals 0?

    And I still don't understand the 3rd one. Is there a way to actually show if it's approaching + or - infinity?
    Look at the left and right hand limits.

    (graph it or look at numerical values if you want)

    comming from the right the limit + infinity

    comming from the left the limit is - infinity

    therefore the limit doesn't exist.
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