📝 Discontinuities And Integrability

📖 From Calculus • 6. Integration • 23 questions available

Practice MCQs for Discontinuities And Integrability. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

Easy Questions

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📝 Sample Questions

Q1. Which of the following best describes a removable discontinuity at \(x = c\)?

🔹 A. The limit does not exist, but the function is defined at \(c\)

🔹 B. The limit exists and equals the function value at \(c\)

🔹 C. The limit exists but differs from the function value at \(c\)

🔹 D. Both the limit and function value are undefined at \(c\)

💡 Difficulty: easy | ✅ Correct: C

Q2. A function \(f\) is defined on \([0,1]\) by \(f(x) = \sin(1/x)\) for \(x > 0\) and \(f(0) = 0\). Which statement is true about its integrability?

🔹 A. \(f\) is not Riemann integrable because it is discontinuous at infinitely many points

🔹 B. \(f\) is Riemann integrable because the set of discontinuities has measure zero

🔹 C. \(f\) is Riemann integrable only as an improper integral

🔹 D. \(f\) is continuous on \([0,1]\)

💡 Difficulty: medium | ✅ Correct: B

Q3. A dragster's velocity over time \(t\) (seconds) is given by \(v(t) = 4t^3 - 12t^2 + 9t + 2\). What is the total distance traveled from \(t = 0\) to \(t = 3\)?

🔹 A. 44 units

🔹 B. 46 units

🔹 C. 48 units

🔹 D. 50 units

💡 Difficulty: hard | ✅ Correct: D

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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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