📝 Infinite Limits Rigorous

📖 From Calculus • 2. Limits and Continuity an Introduction • 38 questions available

Practice MCQs for Infinite Limits Rigorous. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-12

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Q1. What does \(\lim_{x\to a} f(x) = +\infty\) mean rigorously?

🔹 A. For every \(M>0\), there exists \(\delta>0\) such that \(f(x)>M\) if \(0<|x-a|<\delta\)

🔹 B. For every \(M>0\), there exists \(\delta>0\) such that \(f(x)<M\) if \(0<|x-a|<\delta\)

🔹 C. For every \(M<0\), there exists \(\delta>0\) such that \(f(x)>M\) if \(0<|x-a|<\delta\)

🔹 D. For every \(M>0\), there exists \(\delta>0\) such that \(f(x)=M\) if \(0<|x-a|<\delta\)

💡 Difficulty: easy | ✅ Correct: A

Q2. What is the geometric meaning of \(\lim_{x\to a} f(x) = +\infty\)?

🔹 A. The graph approaches the vertical line \(x=a\) and rises without bound

🔹 B. The graph approaches the horizontal line \(y=a\)

🔹 C. The graph approaches the vertical line \(x=a\) and falls without bound

🔹 D. The graph approaches the line \(y=x\)

💡 Difficulty: medium | ✅ Correct: A

Q3. What is the rigorous definition of \(\lim_{x\to a^+} f(x) = +\infty\)?

🔹 A. For every \(M>0\), there exists \(\delta>0\) such that \(f(x)>M\) if \(0<x-a<\delta\)

🔹 B. For every \(M>0\), there exists \(\delta>0\) such that \(f(x)>M\) if \(-\delta<x-a<0\)

🔹 C. For every \(M<0\), there exists \(\delta>0\) such that \(f(x)>M\) if \(0<x-a<\delta\)

🔹 D. For every \(M>0\), there exists \(\delta>0\) such that \(f(x)<M\) if \(0<x-a<\delta\)

💡 Difficulty: hard | ✅ Correct: A

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