Average Values. Find the average value of the function $f(x)=24x^2+8x+1$ on the interval $\frac{n}{2},2n.$ Write your answer as $f_{\text{a}\text{v}\text{g}}=P(n)$ for some polynomial, and then calculate the limit as $n$ goes to infinity of $\frac{f_{\text{a}\text{v}\text{g}}}{n^2}.$

AVERAGE ON $[\frac{n}{2},2n],f_{\text{a}\text{v}\text{g}}=P(n)=$

LIMIT: $\underset{n}{lim}\frac{P(n)}{n^2}=$

WORK: