# Prove P(x) >= M

$P(x) = a_nx^n +a_{n-1}x^{n-1} + \ldots + a_1x + a_0,$ n>=1
Clearly, as $x\to\infty,\ a_nx^n\to\infty$. Show that, as x --> infinity, $P(x)\to\infty$ by showing that, given any positive number M, there exists a positive number K such that if x>=K, then P(x) >=M.
(Hint: you might wish to choose $K_i>0$ such that
$|a_{n-i}/x^i|< a_n/2n$ when $x > K_i$ and then take the largest of the $K_i$. )