📝 Differentiability and Continuity

📖 From Calculus • 3. The Derivation • 28 questions available

Practice MCQs for Differentiability and Continuity. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-13

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📝 Sample Questions

Q1. What does Theorem 2.2.3 state?

🔹 A. Differentiability implies continuity

🔹 B. Continuity implies differentiability

🔹 C. Differentiability and continuity are equivalent

🔹 D. Differentiability implies discontinuity

💡 Difficulty: easy | ✅ Correct: A

Q2. Prove: If \(f\) is differentiable at \(x_0\), then \(\lim_{x\to x_0} f(x) = f(x_0)\).

🔹 A. Use \(f(x)-f(x_0) = \frac{f(x)-f(x_0)}{x-x_0}\cdot(x-x_0)\)

🔹 B. Use the definition of continuity

🔹 C. Use the mean value theorem

🔹 D. Use the intermediate value theorem

💡 Difficulty: medium | ✅ Correct: A

Q3. If \(f\) is continuous at \(x_0\), then \(f\):

🔹 A. May or may not be differentiable at \(x_0\)

🔹 B. Must be differentiable at \(x_0\)

🔹 C. Cannot be differentiable at \(x_0\)

🔹 D. Is differentiable everywhere

💡 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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