**UNIT-1: Sequences and Limits**
1. **State and prove the Sandwich Theorem (or Squeeze Theorem) for sequences.**
2. **State and prove Cauchy's First Theorem on Limits.**
3. **"Every convergent sequence is bounded." Is the converse true? Justify your answer.**
1. **State and prove the Leibniz Test for alternating series.**
2. **State and prove Cauchy's \(n\)-th Root Test for convergence of series.**
3. **State and prove D'Alembert's Test (or Ratio Test) for convergence of series.**
### **UNIT-3: Continuity and Functions**
1. **Discuss the continuity of the function \(f\) where \(f(x) = |x| + |x - 1|\) at \(x = 0\) and \(x = 1\).**
UNIT-4: Mean Value Theorems**
1. **State and prove Rolle's Theorem.**
2. **State and prove Lagrange's Mean Value Theorem (or First Mean Value Theorem).**
3. **State and prove Cauchy's Mean Value Theorem (or Second Mean Value Theorem).**
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### **UNIT-5: Integral Calculus**
1. **State and prove the Fundamental Theorem of Integral Calculus.**
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