← Back to 2. Limits and Continuity an Introduction

📝 One Sided & Two Sided Limits Relationship

📖 From Calculus • 2. Limits and Continuity an Introduction • 80 questions available

Practice MCQs for One Sided & Two Sided Limits Relationship. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-12

Easy Questions

Medium Questions

Hard Questions

📝 Sample Questions

Q1. For a two-sided limit \(\lim_{x\to a} f(x)\) to exist, what must be true?

🔹 A. \(\lim_{x\to a^-} f(x)\) must equal \(\lim_{x\to a^+} f(x)\)

🔹 B. \(f(a)\) must be defined

🔹 C. The function must be continuous

🔹 D. The limit must be finite

💡 Difficulty: easy | ✅ Correct: A

Q2. If \(\lim_{x\to a} f(x) = L\), then which statement is TRUE?

🔹 A. \(\lim_{x\to a^-} f(x) = \lim_{x\to a^+} f(x) = L\)

🔹 B. \(f(a) = L\)

🔹 C. \(f\) is continuous at \(a\)

🔹 D. \(\lim_{x\to a} f(x)\) may not exist

💡 Difficulty: medium | ✅ Correct: A

Q3. What is \(\lim_{x\to 0} \frac{\sin x}{x^2}\)?

🔹 A. 0

🔹 B. 1

🔹 C. \(\infty\)

🔹 D. Does not exist

💡 Difficulty: hard | ✅ Correct: D

⬆️ View all questions in the quiz below

🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Inverse Functions

🚀 Start Quiz 📝 Practice Mode