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📝 Logarithmic Forms Of Inverse Hyperbolic Functions

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 22 questions available

Practice MCQs for Logarithmic Forms Of Inverse Hyperbolic Functions. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

6
Easy Questions
10
Medium Questions
6
Hard Questions

📝 Sample Questions

Q1. Which of the following is the correct logarithmic representation of the inverse hyperbolic sine function \\(\\operatorname{arsinh} x\\)?

🔹 A. \\(\\ln\\bigl(x+\\sqrt{x^{2}+1}\\bigr)\\)
🔹 B. \\(\\ln\\bigl(x+\\sqrt{x^{2}-1}\\bigr)\\)
🔹 C. \\(\\ln\\bigl(x-\\sqrt{x^{2}+1}\\bigr)\\)
🔹 D. \\(\\ln\\bigl(\\sqrt{x^{2}+1}-x\\bigr)\\)

💡 Difficulty: easy | ✅ Correct: A

Q2. Solve for \\(x\\): \\(\\operatorname{arsinh} x = \\ln 3\\).

🔹 A. \\(\\frac{3^{2}-1}{2}\\)
🔹 B. \\(\\frac{3^{2}+1}{2}\\)
🔹 C. \\(\\frac{3^{2}-1}{2\\cdot3}\\)
🔹 D. \\(\\frac{3^{2}+1}{2\\cdot3}\\)

💡 Difficulty: medium | ✅ Correct: B

Q3. Prove that \\(\\operatorname{arsinh} x = \\ln\\bigl(x+\\sqrt{x^{2}+1}\\bigr)\\) by solving the equation \\(y=\\sinh t\\) for \\(t\\).

🔹 A. Use the definition of \\(\\sinh\\) and algebraic manipulation
🔹 B. Apply Euler's formula
🔹 C. Differentiate both sides
🔹 D. Integrate both sides

💡 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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