1. The problem is to evaluate each mathematical expression and then list the results from lowest to greatest. 2. Evaluate each expression step-by-step: - Summation: $\sum_{i=2}^3 i = 2 + 3 = 5$ - Exponential: $e^3 \approx 20.0855$ - Factorial: $6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720$ - Definite integral: $\int_3^6 x \, dx = \left[\frac{x^2}{2}\right]_3^6 = \frac{6^2}{2} - \frac{3^2}{2} = \frac{36}{2} - \frac{9}{2} = \frac{27}{2} = 13.5$ - Square root: $\sqrt{9} = 3$ - Fraction involving $\pi$: $\frac{6\pi}{2} = 3\pi \approx 9.4248$ - Logarithm: $\log_4(25) = \frac{\ln 25}{\ln 4} \approx \frac{3.2189}{1.3863} \approx 2.322$ - Fraction: $\frac{3}{9} = \frac{1}{3} \approx 0.3333$ - Infinity symbol $\infty$ represents an unbounded value and is the greatest. 3. Now, list all values from lowest to greatest: $$0.3333, 2.322, 3, 5, 9.4248, 13.5, 20.0855, 720, \infty$$ Final Answer: $$\boxed{\frac{3}{9} < \log_4(25) < \sqrt{9} < \sum_{i=2}^3 i < \frac{6\pi}{2} < \int_3^6 x\,dx < e^3 < 6! < \infty}$$