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.
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.
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!
Suppose that $\displaystyle f(x)=a_mx^m+a_{m-1}x^{m-1}+\dots+a_1x+a_0$ and $\displaystyle g(x)=b_nx^n+b_{n-1}x^{n-1}+\dots+b_1x+b_0$ where $\displaystyle a_m\ne0$ and $\displaystyle b_n\ne0$. Your questions can be answered using the following facts.
If m < n, then $\displaystyle f(x)/g(x)\to0$ as $\displaystyle x\to\infty$.
If m = n, then $\displaystyle f(x)/g(x)\to a_m/b_m$ as $\displaystyle x\to\infty$.
If m > n and $\displaystyle a_m$, $\displaystyle b_n$ have the same sign, then $\displaystyle f(x)/g(x)\to\infty$ as $\displaystyle x\to\infty$.
If m > n and $\displaystyle a_m$, $\displaystyle b_n$ have opposite signs, then $\displaystyle f(x)/g(x)\to-\infty$ as $\displaystyle x\to\infty$.