1. **State the problem:** We want to approximate the area under the curve of the function $f(x) = \frac{3}{x+1}$ from $x=0$ to $x=3$ using a Riemann sum with 3 rectangles and right endpoints. 2. **Formula and explanation:** The Riemann sum with $n$ rectangles and right endpoints is given by: $$ R_n = \sum_{i=1}^n f(x_i) \Delta x $$ where $\Delta x = \frac{b-a}{n}$ is the width of each rectangle, and $x_i = a + i \Delta x$ are the right endpoints. 3. **Calculate $\Delta x$ and right endpoints:** Given $a=0$, $b=3$, and $n=3$: $$ \Delta x = \frac{3-0}{3} = 1 $$ Right endpoints: $$ x_1 = 0 + 1 \times 1 = 1, \quad x_2 = 0 + 2 \times 1 = 2, \quad x_3 = 0 + 3 \times 1 = 3 $$ 4. **Evaluate the function at right endpoints:** $$ f(1) = \frac{3}{1+1} = \frac{3}{2} = 1.5 $$ $$ f(2) = \frac{3}{2+1} = \frac{3}{3} = 1 $$ $$ f(3) = \frac{3}{3+1} = \frac{3}{4} = 0.75 $$ 5. **Calculate the Riemann sum:** $$ R_3 = \Delta x \left(f(1) + f(2) + f(3)\right) = 1 \times (1.5 + 1 + 0.75) = 3.25 $$ 6. **Final answer:** The approximate area under the curve using 3 rectangles and right endpoints is: $$ \boxed{3.25} $$ Note: The problem's given function values and sum differ from the original problem statement's function $f(x) = \frac{3}{x+1}$; the problem's example uses $f(1) = \frac{1}{2}$, $f(2) = \frac{2}{3}$, $f(3) = \frac{3}{4}$ which corresponds to $f(x) = \frac{x}{x+1}$. Using the problem's values: $$ R_3 = 1 \times \left(\frac{1}{2} + \frac{2}{3} + \frac{3}{4}\right) = \frac{1}{2} + \frac{2}{3} + \frac{3}{4} = \frac{6}{12} + \frac{8}{12} + \frac{9}{12} = \frac{23}{12} \approx 1.9167 $$ This matches the problem's final sum and answer choice (c) $\frac{23}{12}$. Therefore, the correct approximate area is: $$ \boxed{\frac{23}{12}} $$