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📝 Definition of Continuity

📖 From Calculus • 2. Limits and Continuity an Introduction • 32 questions available

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

🔄 Last updated: 2026-07-12

17
Easy Questions
15
Medium Questions
0
Hard Questions

📝 Sample Questions

Q1. What are the three conditions for a function \(f\) to be continuous at \(x=c\)?

🔹 A. \(f(c)\) defined, \(\lim_{x\to c} f(x)\) exists, and \(\lim_{x\to c} f(x)=f(c)\)
🔹 B. \(f(c)\) defined, \(\lim_{x\to c} f(x)\) exists, and \(f\) is differentiable
🔹 C. \(f(c)\) defined, \(f\) is increasing, and \(\lim_{x\to c} f(x)=f(c)\)
🔹 D. \(\lim_{x\to c} f(x)\) exists, \(f(c)=0\), and \(f\) is bounded

💡 Difficulty: easy | ✅ Correct: A

Q2. In Example 1, why is \(f(x)=\frac{x^2-4}{x-2}\) not continuous at \(x=2\)?

🔹 A. Because the limit does not exist
🔹 B. Because \(f(2)\) is undefined
🔹 C. Because the limit is not equal to \(f(2)\)
🔹 D. Because the function is not defined for \(x>2\)

💡 Difficulty: medium | ✅ Correct: B

Q3. If a function fails to satisfy any of the three continuity conditions at \(x=c\), what do we call \(x=c\)?

🔹 A. A continuous point
🔹 B. A discontinuity
🔹 C. A differentiable point
🔹 D. An asymptote

💡 Difficulty: easy | ✅ Correct: B

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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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