Suppose that $Q(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0} $and $P(x)=b_{m}x^{m}+b_{m-1}x^{m-1}+\cdots+b_{1}x+b_{0}.$ How do I find $\lim_{x\rightarrow\infty}\frac{Q(x)}{P(x)}$ and what does the sequence $\frac{Q(k)}{P(k)}$ converge to?
For example, how would I find what the sequence $\frac{8k^2+2k-100}{3k^2+2k+1}$ converges to? Or what is $\lim_{x\rightarrow\infty}\frac{3x+5}{-2x+9}?$
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