1. **State the problem:** Arrange the given values from least to greatest. The values are:\n\n√9, 10/13, \int_2^5 x \, dx, 6!, \frac{4\pi}{6}, \log_3(7), \infty, e^2, \sum_{i=3}^8 i\n\n2. **Evaluate each expression:**\n- \(\sqrt{9} = 3\) because 3\times3=9.\n- \(\frac{10}{13} \approx 0.769\) since 10 divided by 13 is about 0.769.\n- \(\int_2^5 x \, dx \) means calculate the area under \(y=x\) from 2 to 5.\n\text{Calculate it:}\n\int_2^5 x \, dx = \left[ \frac{x^2}{2} \right]_2^5 = \frac{5^2}{2} - \frac{2^2}{2} = \frac{25}{2} - \frac{4}{2} = \frac{21}{2} = 10.5\n- \(6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720\)\n- \(\frac{4\pi}{6} = \frac{2\pi}{3} \approx 2.094\) since \(\pi \approx 3.1416\)\n- \( \log_3(7) \) means the power to which 3 must be raised to get 7.\n\text{Since } 3^1=3 \text{ and } 3^2=9, \log_3(7) \text{ is between 1 and 2}.\n\text{Using change-of-base formula: }\log_3(7) = \frac{\ln 7}{\ln 3} \approx \frac{1.9459}{1.0986} \approx 1.77\n- \(\infty\) is infinity, larger than any finite number.\n- \(e^2 \approx 7.389\) where \(e \approx 2.718\)\n- \(\sum_{i=3}^8 i = 3 + 4 + 5 + 6 + 7 + 8\)\n\text{Calculate sum: } 3+4=7, 7+5=12, 12+6=18, 18+7=25, 25+8=33\n\n3. **Order all evaluated values from least to greatest:**\n\n\( \frac{10}{13} \approx 0.769 < 3 (= \sqrt{9}) < \frac{4\pi}{6} \approx 2.094 < \log_3(7) \approx 1.77 ? \)\nNote: \(\log_3(7) \approx 1.77 < 2.094\)\nCorrect order is:\n\(\frac{10}{13} (0.769) < \log_3(7) (1.77) < \frac{4\pi}{6} (2.094) < \sqrt{9} (3)\)\n\nThen continuing:\n\(3 < \int_2^5 x dx (10.5) < \sum_{i=3}^8 i (33) < e^2 (7.389)?\)\nNote \(e^2 (7.389) < 10.5\) is false, so correct relative order is:\n\(3 < \log_3(7) (1.77) < \frac{4\pi}{6} (2.094) < \sqrt{9} (3)\) but 1.77 < 2.094 < 3\nActually, ordering these values by size:\n\(\frac{10}{13} (0.769) < \log_3(7) (1.77) < \frac{4\pi}{6} (2.094) < \sqrt{9} (3) < e^2 (7.389) < \int_2^5 x \, dx (10.5) < \sum_{i=3}^8 i (33) < 6! (720) < \infty \)\n\n4. **Final list from least to greatest:**\n\$$\frac{10}{13}, \log_3(7), \frac{4 \pi}{6}, \sqrt{9}, e^2, \int_2^5 x \, dx, \sum_{i=3}^8 i, 6!, \infty$$\n