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📝 Definitions Of Hyperbolic Functions

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

Practice MCQs for Definitions Of Hyperbolic Functions. 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 hyperbolic sine function \(\sinh x\)?

🔹 A. \(\frac{e^{x}-e^{-x}}{2}\)

🔹 B. \(\frac{e^{x}+e^{-x}}{2}\)

🔹 C. \(\frac{e^{x}+e^{-x}}{2i}\)

🔹 D. \(\frac{e^{x}-e^{-x}}{2i}\)

💡 Difficulty: easy | ✅ Correct: A

Q2. Compute \(\tanh(\ln 2)\).

🔹 A. \(\frac{3}{5}\)

🔹 B. \(\frac{2}{3}\)

🔹 C. \(\frac{1}{2}\)

🔹 D. \(\frac{3}{4}\)

💡 Difficulty: medium | ✅ Correct: D

Q3. Evaluate \(\displaystyle\int_{0}^{\ln 3}\tanh x\,dx\).

🔹 A. \(\ln(\cosh(\ln 3))\)

🔹 B. \(\ln 3\)

🔹 C. \(\frac12\ln\!\bigl(\frac{4}{5}\bigr)\)

🔹 D. \(\ln\!\bigl(\frac{3+ \sqrt{10}}{2}\bigr)\)

💡 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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