📝 Approximating Ln X Numerically

📖 From Calculus • 6. Integration • 23 questions available

Practice MCQs for Approximating Ln X Numerically. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

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📝 Sample Questions

Q1. What is the definition of the natural logarithm \(\ln(x)\) in terms of an integral?

🔹 A. \(\int_0^x \frac{1}{t} \, dt\)

🔹 B. \(\int_1^x t \, dt\)

🔹 C. \(\int_0^x t \, dt\)

🔹 D. \(\int_1^x \frac{1}{t} \, dt\)

💡 Difficulty: easy | ✅ Correct: D

Q2. A car accelerates continuously such that its speed \(v(t) = v_0 e^{kt}\). If the speed doubles in 5 seconds, which expression gives \(\ln(2)\) in terms of \(k\)?

🔹 A. \(k \cdot 5\)

🔹 B. \(5/k\)

🔹 C. \(k/5\)

🔹 D. \(\ln(k \cdot 5)\)

💡 Difficulty: medium | ✅ Correct: B

Q3. Derive the error term for Simpson's rule applied to \(\int_1^2 \ln(x) \, dx\). Which expression correctly represents the leading error term?

🔹 A. \(-\frac{(b-a)^5}{180} \cdot f^{(4)}(\xi)\)

🔹 B. \(-\frac{(b-a)^4}{180} \cdot f^{(4)}(\xi)\)

🔹 C. \(-\frac{(b-a)^5}{90} \cdot f^{(4)}(\xi)\)

🔹 D. \(-\frac{(b-a)^4}{90} \cdot f^{(4)}(\xi)\)

💡 Difficulty: hard | ✅ Correct: A

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🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Inverse Functions

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