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Math Help - Determining values for a given limit

  1. #1
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    Determining values for a given limit

    Just starting my Calculus I course and very confused as to how to approach these types of questions involving limits. I've attached an image for my online questions. Any help would be greatly appreciated! Thanks in advance.
    Attached Thumbnails Attached Thumbnails Determining values for a given limit-screen-shot-2012-05-22-3.47.13-pm.png  
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  2. #2
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    Re: Determining values for a given limit

    I have expanded the first equation by dividing the numerator and denominator of the rational expression by x^2 ... I have gotten so far:

    (8 / x^2) (x^8 / x^2) - (11 / x^2) (x^4 / x^2) + (4 / x^2)
    __________________________________________________ ____
    (c / x^2) (x^n / x^2) - (8 / x^2) (x^2 / x^2) + (19 / x^2)

    I'm not sure how to solve for c and n at this point!
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  3. #3
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    Re: Determining values for a given limit

    Suppose that f(x)=a_mx^m+a_{m-1}x^{m-1}+\dots+a_1x+a_0 and g(x)=b_nx^n+b_{n-1}x^{n-1}+\dots+b_1x+b_0 where a_m\ne0 and b_n\ne0. Your questions can be answered using the following facts.

    If m < n, then f(x)/g(x)\to0 as x\to\infty.

    If m = n, then f(x)/g(x)\to a_m/b_m as x\to\infty.

    If m > n and a_m, b_n have the same sign, then f(x)/g(x)\to\infty as x\to\infty.

    If m > n and a_m, b_n have opposite signs, then f(x)/g(x)\to-\infty as x\to\infty.
    Thanks from Reckoner and ik2244
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