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📝 Piecewise Defined Limits

📖 From Calculus • 2. Limits and Continuity an Introduction • 53 questions available

Practice MCQs for Piecewise Defined Limits. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-12

15
Easy Questions
26
Medium Questions
12
Hard Questions

📝 Sample Questions

Q1. For piecewise-defined functions, at a point where the formula changes, how should you find the two-sided limit?

🔹 A. Use the formula for all \(x\)
🔹 B. Find one-sided limits first
🔹 C. Use the formula at that point
🔹 D. The limit never exists

💡 Difficulty: easy | ✅ Correct: B

Q2. For \(f(x)=\begin{cases} x^2+1, & x<0 \\ 1-x, & x\ge 0 \end{cases}\), what is \(\lim_{x\to 0} f(x)\)?

🔹 A. 0
🔹 B. 1
🔹 C. 2
🔹 D. Does not exist

💡 Difficulty: medium | ✅ Correct: B

Q3. For \(f(x)=\begin{cases} \frac{1}{x+2}, & x<-2 \\ x^2-5, & x\ge -2 \end{cases}\), what is \(\lim_{x\to -2^-} f(x)\)?

🔹 A. \(+\infty\)
🔹 B. \(-\infty\)
🔹 C. -1
🔹 D. Does not exist

💡 Difficulty: hard | ✅ Correct: B

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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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