📝 Value of δ Not Unique

📖 From Calculus • 2. Limits and Continuity an Introduction • 33 questions available

Practice MCQs for Value of δ Not Unique. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-12

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Q1. Is the value of \(\delta\) in the epsilon-delta definition unique?

🔹 A. Yes, there is exactly one \(\delta\) for each \(\epsilon\)

🔹 B. No, any smaller positive \(\delta\) also works

🔹 C. No, any larger \(\delta\) also works

🔹 D. Yes, \(\delta\) must equal \(\epsilon\)

💡 Difficulty: easy | ✅ Correct: B

Q2. If \(\delta = \epsilon/3\) works for a limit proof, then which of the following also works?

🔹 A. \(\delta = \epsilon/4\)

🔹 B. \(\delta = \epsilon/2\)

🔹 C. \(\delta = \epsilon\)

🔹 D. \(\delta = 2\epsilon\)

💡 Difficulty: medium | ✅ Correct: A

Q3. If \(\delta = \min(1, \epsilon/7)\) works in Example 3, which of the following also works?

🔹 A. \(\delta = \min(1, \epsilon/8)\)

🔹 B. \(\delta = \min(2, \epsilon/7)\)

🔹 C. \(\delta = \min(1, \epsilon/6)\)

🔹 D. \(\delta = \min(2, \epsilon/6)\)

💡 Difficulty: hard | ✅ Correct: A

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