📝 The Definition Of Area As A Limit: Sigma Notation

📖 From Calculus • 6. Integration • 22 questions available

Practice MCQs for The Definition Of Area As A Limit: Sigma Notation. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

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📝 Sample Questions

Q1. What does the limit of the areas of inscribed regular \(n\)-sided polygons approach for a unit circle as \(n \to \infty\)?

🔹 A. \(0\)

🔹 B. \(\pi/2\)

🔹 C. \(\pi\)

🔹 D. \(2\pi\)

💡 Difficulty: easy | ✅ Correct: C

Q2. A dragster travels with velocity \(v(t) = 4 - t\) (m/s) from \(t = 0\) to \(t = 3\) s. Which Riemann sum best estimates the distance traveled?

🔹 A. Left‑endpoint sum

🔹 B. Right‑endpoint sum

🔹 C. Midpoint sum

🔹 D. Trapezoidal sum

💡 Difficulty: medium | ✅ Correct: D

Q3. For \(f(x) = \sin x\) on \([0,\pi]\), which sigma expression correctly represents the definite integral as a limit of sums?

🔹 A. \(\lim_{n \to \infty} \sum_{k=1}^{n} \sin\left( \frac{k\pi}{n} \right) \cdot \frac{\pi}{n}\)

🔹 B. \(\lim_{n \to \infty} \sum_{k=1}^{n} \sin\left( \frac{k\pi}{n} \right) \cdot \frac{\pi}{n}\)

🔹 C. \(\lim_{n \to \infty} \sum_{k=1}^{n} \sin\left( \frac{k\pi}{n} \right) \cdot \frac{\pi}{n}\)

🔹 D. \(\lim_{n \to \infty} \sum_{k=1}^{n} \sin\left( \frac{k\pi}{n} \right) \cdot \frac{\pi}{n}\)

💡 Difficulty: hard | ✅ Correct: C

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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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