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- Jan 26, 2012
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Thank your to Chris L T521 for submitting this week's high school level problem!
$p(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0$ and $q(x)=b_mx^m+b_{m-1}x^{m-1}+\cdots+b_1x+b_0$. Show that
\[\lim_{x\to\infty}\frac{p(x)}{q(x)}=\begin{cases} \infty & \text{ if $n>m$}\\ \frac{a_n}{b_m} & \text{ if $n=m$}\\ 0 & \text{ if $n<m$}\end{cases}\]
Remember to read the POTW submission guidelines to find out how to submit your answers!
$p(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0$ and $q(x)=b_mx^m+b_{m-1}x^{m-1}+\cdots+b_1x+b_0$. Show that
\[\lim_{x\to\infty}\frac{p(x)}{q(x)}=\begin{cases} \infty & \text{ if $n>m$}\\ \frac{a_n}{b_m} & \text{ if $n=m$}\\ 0 & \text{ if $n<m$}\end{cases}\]
Remember to read the POTW submission guidelines to find out how to submit your answers!