📝 ERROR IN LOCAL LINEAR APPROXIMATIONS

📖 From Calculus • 4. Topics in Differentiation • 20 questions available

Practice MCQs for ERROR IN LOCAL LINEAR APPROXIMATIONS. 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 relative error in a linear approximation is defined as:

🔹 A. \(|\text{exact}| - |\text{approx}|\)

🔹 B. \(\frac{|\text{exact} - \text{approx}|}{|\text{exact}|}\)

🔹 C. \(|\text{exact} - \text{approx}|\)

🔹 D. \(\frac{|\text{exact} - \text{approx}|}{|\text{approx}|}\)

💡 Difficulty: easy | ✅ Correct: B

Q2. If the error in the linear approximation is \(E(x)\), what is true about \(E(x)\) as \(x \to x_0\)?

🔹 A. \(E(x) \to \infty\)

🔹 B. \(E(x) \to 0\)

🔹 C. \(E(x) \to 1\)

🔹 D. \(E(x)\) is constant

💡 Difficulty: medium | ✅ Correct: B

Q3. The error in the linear approximation \(\sin x \approx x\) for small \(x\) is approximately:

🔹 A. \(\frac{x^4}{24}\)

🔹 B. \(\frac{x^2}{2}\)

🔹 C. \(\frac{x^3}{6}\)

🔹 D. \(x\)

💡 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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