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📝 Slope Fields

📖 From Calculus • 6. Integration • 23 questions available

Practice MCQs for Slope Fields. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

7
Easy Questions
10
Medium Questions
6
Hard Questions

📝 Sample Questions

Q1. What is the slope at the point \((0,0)\) for the differential equation \(\frac{dy}{dx} = y - x\)?

🔹 A. \(0\)
🔹 B. 0
🔹 C. \(1\)
🔹 D. \(-1\)

💡 Difficulty: easy | ✅ Correct: A

Q2. Consider \(\frac{dy}{dx} = x^2 - y\). Near the origin \((0,0)\), which statement best describes the direction of solution curves?

🔹 A. They curve upward because \(x^2\) dominates
🔹 B. They curve downward because \(-y\) dominates
🔹 C. They are nearly horizontal
🔹 D. They spiral around the origin

💡 Difficulty: medium | ✅ Correct: C

Q3. Consider \(\frac{dy}{dx} = \frac{x^2 - y}{x + y^2}\). As \(x \to \infty\), what does the slope approach for bounded \(y\)?

🔹 A. \(0\)
🔹 B. \(1\)
🔹 C. \(-1\)
🔹 D. Infinity

💡 Difficulty: hard | ✅ Correct: A

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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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