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Math Help - Infinity limits

  1. #1
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    Infinity limits

    I'm suppose to solve for c and n.
    Could someone please give me some advice on how to start ?
    Any advice/hints are greatly appreciated.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    For rational functions the limit at + or - infinity is the ratio of the highest
    powered terms.

    This should be enough to answer the question.
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  3. #3
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    Quote Originally Posted by Calculus26 View Post
    For rational functions the limit at + or - infinity is the ratio of the highest
    powered terms.

    This should be enough to answer the question.
    Could you explain it a litte bit more please? I don't understand.
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  4. #4
    MHF Contributor Calculus26's Avatar
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    looking at the ratio you have of highest powered terms you have

    lim(10*x^7)/(cx^n) = 10/10 = 1

    what do c and n have to be?
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  5. #5
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    Quote Originally Posted by Calculus26 View Post
    looking at the ratio you have of highest powered terms you have

    lim(10*x^7)/(cx^n) = 10/10 = 1

    what do c and n have to be?
    I got it ! Thanks its 10 and 7. But why do we just ignore everything else?
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  6. #6
    MHF Contributor Calculus26's Avatar
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    the key is at infinity

    limc/x^n = 0

    if you divide through by the highest poweed terms everything goes to 0 except the leading terms

    for Eg

    lim(2x^3 + 3x + 1)/(x^3 +2)

    =lim [x^3( 2 + 3/x^2 +1/x^3)/[x^3(1+2/x^3)]

    =lim (2+3/x^2 +1/x^3)/(1+ 2/x^3)

    = (2+0+0)/(1+0) = 2

    so imsteas of dividing through by the highest powered terms each time we recognize we can just consider the ratio of highest powered term.

    This is also true if the highest powers on top and bottom are different just consider the ratio
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