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Math Help - one more evaluating limits

  1. #1
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    one more evaluating limits

    I thought I could do this one on my own - I was wrong

    lim (3x^2 - x-2)/(5x2 +4x +1)
    x->infinity

    I know the top line can be factored down to (3x+2)(x-1) but even with this I can't figure out what to do with the bottom half. Please help me.

    Thanks in advance
    this calculus beginner
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  2. #2
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    Quote Originally Posted by calcbeg View Post
    I thought I could do this one on my own - I was wrong

    lim (3x^2 - x-2)/(5x2 +4x +1)
    x->infinity

    I know the top line can be factored down to (3x+2)(x-1) but even with this I can't figure out what to do with the bottom half. Please help me.

    Thanks in advance
    this calculus beginner
    The best way to do this is divide everything by x^2 ( top and bottom )


    lim (3x^2 - x-2)/(5x2 +4x +1)
    x->infinity

    lim (3x^2 - x-2)/(x^2) /(5x2 +4x +1)/(x^2)
    x->infinity


    lim (3 - 1/x-2/x^2)/(5 +4/x +1/x^2)
    x->infinity
    As x ---> inifinity

    1/x --> 0
    4/x --- > 0
    2/x^2 --- > 0

    1/x^2 --> 0

    3 ---> 3

    5---> 5

    lim (3 - 1/x-2/x^2)/(5 +4/x +1/x^2) = 3/5
    x->infinity
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