limx→∞a0xn+a1xn−1+⋯+anb0xm+b1xm−1+⋯+bm={∞ (n>m)a0b0 (n=m)0 (n<m)\lim_{x\to\infty}\frac{a_0x^n+a_1x^{n-1}+\cdots+a_n}{b_0x^m+b_1x^{m-1}+\cdots+b_m}=\begin{cases} \infty\ \ (n>m)\\\frac{a_0}{b_0}\ \ (n=m)\\0\ \ \ \ (n<m)\end{cases}limx→∞b0xm+b1xm−1+⋯+bma0xn+a1xn−1+⋯+an=⎩⎨⎧∞ (n>m)b0a0 (n=m)0 (n<m)
