$(1$ point$)$ Consider the function $f(x)=\frac{x^2}{4}+7$

In this problem you will calculate ${\displaystyle \underset{0}{\overset{3}{}}}(\frac{x^2}{4}+7)dx$ by using the definition

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx=\underset{n}{lim}[{\displaystyle \underset{i=1}{\overset{n}{}}}f(x_i)x]$

The summation inside the brackets is $R_n$ which is the Riemann sum where the sample points are chosen to be the right$-$hand endpoints of each sub$-$interval.

Calculate $R_n$ for $f(x)=\frac{x^2}{4}+7$ on the interval $0,3$ and write your answer as a function of $n$ without any summation signs. You will need the summation formulas in Section $5$ of your textbook.

$R_n=$

$\underset{n}{lim}{R}_n=$

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