Determining values for a given limit

**ik2244** · May 22nd 2012, 02:50 PM

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.

**ik2244** · May 22nd 2012, 03:06 PM

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)
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(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!

**emakarov** · May 22nd 2012, 03:11 PM

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 $x\to\infty$ .

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