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📝 Graphs Of The Hyperbolic Functions

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 23 questions available

Practice MCQs for Graphs Of The 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. Do hyperbolic functions have a fundamental period?

🔹 A. No, they are not periodic

🔹 B. Yes, period \(2\pi\)

🔹 C. Yes, period \(\pi\)

🔹 D. Only \(\cosh\) is periodic

💡 Difficulty: easy | ✅ Correct: A

Q2. Find the area between \(y=\sinh x\) and the x‑axis from \(x=0\) to \(x=1\).

🔹 A. \(\cosh 1-1\)

🔹 B. \(\sinh 1\)

🔹 C. \(\frac12(\cosh 1-1)\)

🔹 D. \(1-\cosh 1\)

💡 Difficulty: medium | ✅ Correct: D

Q3. Prove that \(\frac{d}{dx}\operatorname{sech} x = -\operatorname{sech} x\,\tanh x\).

🔹 A. Differentiate using quotient rule

🔹 B. Use definition \(\operatorname{sech}x=1/\cosh x\)

🔹 C. Apply chain rule on \(\cosh^{-1}x\)

🔹 D. All of the above

💡 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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