📝 LOCAL LINEAR APPROXIMATION; DIFFERENTIALS

📖 From Calculus • 4. Topics in Differentiation • 26 questions available

Practice MCQs for LOCAL LINEAR APPROXIMATION; DIFFERENTIALS. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-14

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📝 Sample Questions

Q1. The accuracy of a local linear approximation generally:

🔹 A. Is always exact

🔹 B. Decreases as \(x\) moves farther from \(x_0\)

🔹 C. Is independent of the distance from \(x_0\)

🔹 D. Increases as \(x\) moves farther from \(x_0\)

💡 Difficulty: easy | ✅ Correct: B

Q2. Approximate \(\sqrt{1.1}\) using the linear approximation at \(x_0 = 1\).

🔹 A. \(1.05\)

🔹 B. \(1.1\)

🔹 C. \(1.2\)

🔹 D. \(1.01\)

💡 Difficulty: medium | ✅ Correct: A

Q3. Approximate \(\sin 2^\circ\) using the linear approximation.

🔹 A. \(0.0349\)

🔹 B. \(0.035\)

🔹 C. \(0.0348995\)

🔹 D. \(0.0349066\)

💡 Difficulty: hard | ✅ Correct: D

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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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