Continuity and Differentiability for JEE Mathematics

Mastering calculus is one of the most critical steps to succeeding in competitive engineering exams like the JEE. Understanding how functions behave, where they break, and how they change is essential for solving high-weightage calculus problems. This text-based course offers a structured approach to continuity and differentiability, balancing rigorous mathematical theory with step-by-step problem-solving strategies. You will move from foundational definitions of limits to analyzing complex piecewise functions, identifying points of non-differentiability, and applying core theorems with precision. What you'll learn: 1. Understand foundational concepts of limits, left-hand and right-hand limits, and functional behavior. 2. Define and analyze continuity at a point, over an interval, and for piecewise functions. 3. Master differentiability rules and identify points where a derivative fails to exist. 4. Apply core calculus theorems including Rolle's Theorem and the Mean Value Theorem to exam-style problems. 5. Analyze functions graphically to quickly identify discontinuities and sharp corners. 6. Practice step-by-step mathematical proofs and algebraic techniques used in competitive exams. We begin with essential terminology, basic definitions, and graphical interpretations of limits. From there, you will progress through clear, written explanations of continuity and differentiability, supported by detailed walkthroughs of classic exam-style problems. This course is designed for high school students, engineering aspirants preparing for competitive exams like the JEE, and anyone looking to strengthen their foundational calculus skills. No advanced calculus knowledge is required to start. Start reading today to build your mathematical confidence and master calculus fundamentals.