Calculus Foundations: Continuity and Differentiability for JEE

Calculus forms the backbone of advanced mathematics, and mastering continuity and differentiability is crucial for succeeding in competitive engineering exams. This text-based course guides you from the fundamental concepts of limits to advanced differentiability theorems, ensuring you build a robust analytical foundation. You will learn to: • Understand the formal definitions of limits, continuity, and differentiability. • Analyze the behavior of functions at critical points using algebraic methods. • Apply core calculus theorems, including the Intermediate Value Theorem and Mean Value Theorem. • Solve complex continuity problems involving piecewise and composite functions. • Practice identifying points of non-differentiability with structured written exercises. The course begins with essential terminology and basic limit concepts before moving into rigorous proofs, continuity tests, and differentiability analysis. It is designed for beginners and exam aspirants looking to build a strong mathematical foundation from scratch. Start reading today to master the core calculus concepts needed for competitive exams.